Emma Thompson was on a ship recently, bound for the Arctic, with 37 crew and her 14-year-old daughter, Gaia, part of a Greenpeace mission to highlight global warming. She has done a lot of trips like this, to Africa and south-east Asia – "raising awareness", as the exhausted phrase goes – but the ship cleaving through ice seemed particularly apt. Thompson, at 55, is regarded as formidable in almost the Edwardian style, the actor-activist more concerned with the cause than with what you might think of her – or, for that matter, with the niceties of the charity world. "When a disaster occurs," she says, "there can be a rather unsavoury rush to plant the flag of your NGO in the nearest head of whoever's surviving." She will not bite her tongue for anyone.

Nor, for the most part, will she play the movie star card. We are in Thompson's work space in a semi-detached house in suburban north London, near where she grew up and where her family still lives. She looks like a graduate student in a Greenpeace sweatshirt, torn jeans, owlish glasses and trainers, her face fresh without makeup – an observation that, after spending an hour with Thompson, one hesitates to make for fear of letting the side down. Still, she is an actor, and pulls another version of herself out of the hat when necessary, appearing on talkshows and at awards ceremonies to promote, in the US at least, a highly stylised Englishness that the Americans find charming and the English, perhaps, find a little de trop.

"Well, it's just energy. It's performance energy," she says. "It's not what you do, and you might regard it with some horror, but it's what I do. And it's what pantomime performers have done for centuries in our country. I don't have to do too much that's truly idiotic."

This is true. Thompson's roles have, over the years, inspired an unusual devotion. A week before our meeting, I was at a US immigration office in New York where a harried, thirtysomething officer insisted on having a reason for my trip, and when I gave him one, transformed before my eyes. Sense And Sensibility, he said, was his favourite film. I thought he was going to cry. Even at 20 years' distance, Thompson's Elinor Dashwood in the Ang Lee adaptation of Austen's novel – especially the moment where she finds out that Edward Ferrars is not, after all, married – does something weird to one's system; so, too, her Margaret Schlegel in Howards End, and the scene (the only good one) in Love Actually, when she crumples on discovering her husband Harry (Alan Rickman) is lusting after someone else. Thompson is ordinarily so brisk, so seemingly sorted and amused, that when she goes, we all go.

Anyway, she is in a mildly brisk mode today, on a mission to inform us about the planet which, of course, we should be thoroughly engaged with, but who has the time, and aren't there a million other things to be worried about? "It's your grandchildren," she says. "You've got skin in the game, mate. And if my daughter is lucky enough to have children, if she wishes them, and I have grandchildren, these are the people who are going to be dealing with the mess. So unless we get to grips with this instead of just wibbling on, it's going to be really hard."

The nine-day voyage to the Smeerenburg glacier, part of the Svalbard archipelago in the Arctic Ocean, was designed to flag up the environmental threats posed by climate change and oil drilling. "We have a dependency, in the same way we had a dependency on tobacco until we realised it killed us. Fossil fuels were a really good idea at the time. But they're not a good idea any more. It's so hard, because you've got corporations with trillions and trillions of dollars who see things that are trapped in the Earth's crust as their inheritance. And I think one of the reasons people zone out is they feel guilty and helpless."

At one point in the Guardian's film of the trip, while standing on the ice in full Arctic gear, she holds up a sign addressed to Tony Abbott, the Australian prime minister who, though he has since softened his stance, once referred to climate change science as "crap". (The sign says: "Tony Abbott Climate Change is REAL I'm Standing In It").

Any word from his office?

"No, no, sadly not. I'd be very happy to have a chat to Tony about his attitudes to women and abortion. Look at the things that Tony Abbott has said – oh, he's a corker." She bursts out laughing. "Tragic." It's embarrassing, I say. Thompson says drily: "People are embarrassing."

Embarrassment is one of the emotions she plays well. Also, indignation and bafflement. Remember her in The Remains Of The Day, trying to wrangle a human response out of Anthony Hopkins' repressed butler? In her most recent role, as PL Travers in the biopic Saving Mr Banks, she went the full Edith Evans with a performance that tipped, here and there, into parody. But Thompson is always fascinating to watch, the frank intelligence of her performances somehow acknowledging the absurdity of the whole acting exercise without ever quite killing off suspension of disbelief.

She will talk effectively about dwindling roles for women in their 50s, but is affronted by suggestions – even indirect ones – that she downplay her age. While on ship, her daughter made her tweet, something that doesn't come naturally. "No, no, I wouldn't dream of it, normally. It's not my generation."

Really?

"No. I'm 55. It's not my thing at all." She says this very firmly, as if countering a wrong but widely held assumption about 55-year-olds in general. "I mean, it took me ages to get used to using a computer."

She is having a great decade, what with the success of the Nanny McPhee franchise, and plaudits for Mr Banks. But don't be fooled, she says. The reason she said yes to Greenpeace (apart from the fact that a great friend asked her) is that it met the stringent criteria she now applies to all projects: "Is the subject right and fascinating, and can I bring every best energy I have to it? Especially now, when time's running out. It's a different patch of life, your 50s."

She feels that?

"Yes. Absolutely. Sorry. Not in a horrible way, but…"

I thought 50 was the new 35?

"Can I just say, very loudly, bollocks. If you look after yourself and you're healthy, then you'll have the energy to do things. But not to recognise getting older for what it is? I do think the infantilisation of our generation is one of the huge issues of our time. People wanting to be 35 when they're 50 makes me think: why? Why don't you be 50 and be good at that? And also embody the kinds of choices that are sustainable at that age."

What sort of choices? "Well, I see people starting life over and over again. And you want to say: just go deeper into the one you've got. Because you can skim very easily. It's set up for that because we're such a disposable society. And I think that relationships are regarded as more disposable than they were, and that's short-sighted of us."

Thompson is married to the actor Greg Wise, whom she met on the set of Sense And Sensibility. Theirs is perceived to be a good union; I tell her that before our meeting, a friend said one of the reasons she admires Thompson is that she "has a great marriage". She gives me a rather dry look. "I think the first 20 years are the… bedrock. And then you can start having a good time."

How many years has she been married?

She smiles. "Nineteen."

As a child, Emma Thompson was regarded as bossy. She has said, in interviews, that this impression continued into adulthood and that some, in the past, have found it hard to deal with – "mentioning no names, but my first husband". (She was married to Kenneth Branagh for six years from 1989.) Now, she says, "I saw 'bossy' used in reference to a man recently, which I thought was very encouraging. I wouldn't refer to myself as bossy in the normal run of things, but of course I was called bossy, constantly, when I was younger. As was and is everyone, as Rebecca West would say, who has an opinion that doesn't chime with that of a doormat."

Her mother, Phyllida Law, and her father, Eric Thompson, were in the entertainment business, a jobbing actor and director. Their two girls, Emma and Sophie, grew up in the mild bohemia of 1970s north London, which Law has written about in two very charming memoirs, Notes To My Mother-In-Law and How Many Camels Are There In Holland? The kitchen table at dinner was a lively place. "We were surrounded by writers and directors and actors, so there was a lot of talk about theatre. But not, I would imagine, the sort of talk that was around Peter Brook's table. It was humbler, really. We talked about books, a bit. Mum's a great reader. But it wasn't a political atmosphere, in the way that our house now has a political atmosphere. I don't think I discovered politics of that kind until I was at uni."

Both parents had to work, as did Thompson from her early 20s; one of the most useful things she learned from her parents is that it is OK to be out of the limelight. "Sometimes there was money and sometimes there wasn't. They weren't particularly famous, none of their friends was famous. It was just a job. It's just my job. Fame is a completely accidental by-product. I don't have any feeling of, you've got to keep your face up there."

After Gaia was born, Thompson scaled back for many years. When she did re-engage, she was lucky to have Wise around to pick up the slack at home. "I could never have done any of my work that involved filming otherwise. Writing's great, but going off to work on something like Saving Mr Banks I couldn't have done. I'd have had to take her with me or something."

Presumably she could go off with a clear conscience, though, because Gaia was with her dad. "Not really. There's always guilt."

For the last few years, Thompson has been working on first the writing, then the filming of Effie Gray, the story of the 19th-century art critic John Ruskin and his long-suffering wife, played by Dakota Fanning; Thompson plays the imperious Lady Eastlake and Greg Wise plays Ruskin. The film was stuck in legal purgatory for years while Thompson successfully defended two plagiarism suits brought by American writers. It's a strange film, slow and a little thin, but beautifully filmed and the performances are terrific – especially from Wise, who makes Ruskin's rejection of his wife and adherence to his mother (Julie Walters) skin-crawlingly creepy. It's very British, in lots of ways, full of people failing to say what they think or mean, although, as Thompson points out, the Americans can be just as bad. "They're often very dishonest, especially in my business. 'Oh, yeah, great, you were fabulous!'" The Brits probably have it worse, though. "I think the British can be very twisted about their genuine feelings. Have you read [Edward St Aubyn's] Patrick Melrose novels? Oh my god! Talking of false identities and people's disguises."

To Thompson's delight, Gaia loved the trip to the Arctic, and found the people on ship deeply sympathetic. They were all ages, all backgrounds, some optimists, some pessimists, which Thompson liked. (She is, unusually for someone promoting a cause, deeply sceptical about the aid world. "I liked the fact that you weren't with a load of people saying, 'We're going to save the planet!' The question of whether it's a form of make-yourself-feel-better tourism I think is a very fair one.") Gaia, meanwhile, said, "'I've found my tribe.' And I knew exactly what she meant."

As a teenager of roughly the same age, Thompson was "very loud and angry". In the Guardian's video, her daughter comes across as a thoroughly nice kid. "Well, yeah, let's hope so. She's wonderful and I think she's fantastic. I think the proof will be on the analyst's couch in 30 years' time, if that occurs. I don't think so, though, because I think of Gaia and Tindy as being very much hand-reared. They've been checked, and picked out, like a little garden. They haven't been handed over to anyone. There's a lot of soil work."

Tindy is Thompson's 27-year-old adopted son, a former child soldier from Rwanda whom she and Wise met at a Refugee Council event when he was 16. He has accompanied her on many aid trips and is now a human rights lawyer. Gaia was just two when he came into their lives, and the two regard each other as siblings, absolutely, she says. "For Tindy, Gaia's incredibly valuable, because she's a proper sister. And he drives her mad and they fight. They fight! Which is brilliant. When that happens, I'm secretly thrilled."

At Cambridge in the early 1980s, Thompson shaved her head and grunged out, as the times permitted. Her feminism was uncompromising and it stayed that way after her hair grew back. It is absurd that, by talking without caveat about sexism, she is considered almost eccentrically radical by the standards of her industry. (She traces the destruction of the Arctic – the fact that we're "fucking the Earth over right, left and centre" – to patriarchal standards set during the industrial age. Most Hollywood actresses would rather die than use the word "patriarchy".)

"Yes, it does baffle me. I don't understand. When you say, 'But feminism means equal rights for women' – sorry, what's the problem? You think it's done? Then think again and inform yourselves, because it isn't done. Don't be daft about it. So what's the issue? Is it that there have been feminists who have said things that shock and appal you?"

Perhaps other actresses think they won't get jobs. "Well, I would not be in work if that was the case. It's very, very odd. I've worked with some young, brilliant women whom I would consider feminists, who don't like to use the word."

Does she remonstrate with them? "Yes. I say, why? It seems to be out of fashion. Surely it's a bottom line thing that has nothing to do with fashion, one way or another."

Parenting teens, Thompson says, strikes her as much harder than stewarding younger children. She and her oldest friend from university took Gaia and three other teens to the Reading festival last month, whereupon "the most important thing is that they know you're there, but that you can be picked up and used as and when needed. I think people sometimes think, oh, they're teens now, they're up and running. But this is the crucial time; when they're little, they just need feeding and cuddling. But not this later stuff. You have to be around."

She thinks back to when she was 15, "reading Jackie fucking magazine. Reading articles like How To Find Your Man And Keep Him. I was wading through a huge heap of insidious twaddle." The insidious twaddle available to today's teens is much more pervasive. Like most sensible parents, Thompson keeps the computer in the kitchen, but you can't police your teen's phone. The sheer weight of sexual imagery to which they are exposed, she believes, means people growing up now "don't have any connection to their own sexuality. It'll be our children who will tell us later: why the fuck didn't you do something about this? Do you know I haven't had an erection since 1989 or whatever?"

Has Thompson's strength of feeling, her willingness to campaign, interfered with her work? Would she use a film to proselytise?

"Give me an example of a proselytising film. In The Name Of The Father or something?"

Well, except that was a great movie. Could a script light her political fire but still be a bad film? "No, no, no, no, no. I get offered a ton of political stuff, and a lot of the time it's not good enough. There aren't very many films that are truly political and truly great. The Lives Of Others, City Of God. Some of Mike Leigh's are wonderful, and Ken Loach's can be fantastic, but sometimes a bit too proselytising for me. I need to be surprised. It's like reading Victor Hugo's Misérables. I got exhausted by agreeing with him. I thought, yes, I know, it's awful, the poor get shat on." She chuckles.

She was heavily criticised, and called an IRA sympathiser, for In The Name Of The Father, Jim Sheridan's 1993 biopic of the Guildford Four, in which she played defence lawyer Gareth Peirce. And there was criticism when she publicly opposed the first Gulf war.

Not all of her judgment calls are right, mind you; Thompson added her name to the ill-advised petition in support of Roman Polanski some years ago. "Yes, but then I had to take my name off it. Mike Nichols rang me up and said, sign this, and sent me a documentary about the utterly appalling [judicial] process. Made by a woman. And I thought, OK, well it's a tricky one. Then I spoke to a woman at Tindy's university who said no, rape is rape, and I thought about it and thought, mmm, yeah. Yeah. You're right. And it was such a messed up process of justice, it was rotten. But rape is rape. And you look at what's been going on recently here with Operation Yewtree and it makes your eyes water."

Gaia pops her head round the door, very much following in her mum's sartorial style in DMs and a jacket that would look great on a demo. She is off out for the day. "Are you going to be warm enough, mate?" Thompson says cheerfully. "Take a scarf."

She turns back to the kitchen table. Her political interests, she assumes, are tolerated in the US, "because they know I'm going to go away. I'm not going to live there and fiddle with their menfolk. Or indeed their women. I don't know." And she half-shrugs, as if to say, either way, it doesn't make the blindest bit of difference.

• Effie Gray goes on general release next month.

Emma Thompson will be speaking at the People's Climate March in London on 21 September, part of a global day of action on the climate crisis. To sign the petition in support of her campaign, go to savethearctic.org/emma

• This article was edited on 15 September 2014, to remove the photo-shoot clothing credits in the endnote that jarred unnecessarily with the content.