You would think that there is nothing that Joan Rivers can do to shock any more. She started her career making jokes about abortions, and has made cracks about her husband's suicide. She is famously potty-mouthed (she was thrown off the daytime show Loose Women in 2008 after describing Russell Crowe as a "fucking shit") and there is nothing outrageous that can be said about her extensive cosmetic surgery that she hasn't already said herself.

So it comes as a bit of a shock to find that in person she is so surprisingly quiet. The rasp to her voice that can make her vitriolic and brassy on stage is softer; she seems gentle and excessively polite, offering coffee from a silver pot before sitting down, primly straight-backed, on a sofa in one of the glamorously formal rooms at the Ritz.

It is obvious why she always stays here when she is in London once you have seen how she has decorated her grand, ornate New York apartment in a new documentary, A Piece of Work. "Marie Antoinette would have lived here," Rivers says at one point, "if she had the money."

Throaty cackle

The film, which follows Rivers over 14 months, and was directed by Ricki Stern and Annie Sundberg, whose previous films include a documentary on Darfur, has already won critical praise and an award at the Sundance film festival. "I went there with two speeches," she says. "The first was, 'look, I had nothing to do with it' and then we started to win awards, so I changed my speech to 'I always knew. It was all me'." She laughs, a low throaty cackle. Why did she agree to do the film? The only reason, she insists, was that she knows Stern's mother. It may turn out to be one of the best decisions of her life.

It isn't a pretty portrait, but it is bracing and a slap in the face to anyone who thinks Rivers has lost her edge, and and is merely a target for ridicule with her cosmetic surgery and costume jewellery range. The Rivers that we get to see is vulnerable, ruthless, ambitious, caring, bitter and relentlessly sharp.

Her humour pushes at the limit of acceptability, and occasionally falls over it: at one point, she runs one joke – is it OK to refer to Michelle Obama as "Blackie O"? – past her entourage (answer: no). How much control did she have over what went in the film? "None," she says, although she admits she asked them to remove some things she said about her husband's suicide because her daughter, Melissa, had asked her to.

Rivers makes a fabulous interviewee – one anecdote begins "I was at a dinner with Laurence Olivier" – and her face is fascinating; her eyes disappear beneath the contours of her unnaturally smooth, plump skin, like raisins sunk into dough. She is flawlessly made-up, dressed all in black.

The overriding impression that comes across in the film is how hard she works, and how terrified she is that the work is about to disappear. "Constantly," she says now. "Things can be taken away – my Fox show was taken away overnight. There is insecurity but that's what keeps you on your toes." It's the reason she appears to say no to very little – she still performs standup most weeks, she peddles her jewellery on the shopping channel QVC, she has a show called How'd You Get So Rich? in which she interviews self-made millionaires, and she has just finished a reality show called Mother Knows Best? with Melissa.

At 77, there is no sign that she will slow down. "I'm one of the lucky ones," she says. "It's what I love. A painter can go and paint, a cook can still make a cake. But what, am I going to tell a joke to myself? If they are not wanting to come and listen to me then I don't have it any more, it's gone, and that would be sad because I adore that. I love the performing and the creating."

In the documentary, Melissa, Rivers's only child, describes The Career as being like a sibling. "Totally," says Rivers. "It was Melissa first, the career second, and my husband probably third. But it also supported us." She smiles. "It was a child with a big trust fund."

Jokes come from everywhere and can strike at any moment. She rummages in her handbag and pulls out an old airline ticket. "I was thinking about memorial monuments," she says, looking down at writing scrawled on the ticket, "so I was going to say: 'after my husband's suicide, I loved him so much I wanted to get a beautiful memorial stone so I spent $250,000'." She holds out her ring finger. "'And here it is!'" We both laugh (luckily). "I never throw anything out of my bag because everything has crap written all over it."

Is there anything she won't joke about? In the film, she is shown being heckled at a show by a man, clearly distressed, who has taken offence at a joke about Helen Keller. He shouts to Rivers on stage that his son is deaf. At the show, Rivers goes on the attack. "I rarely get heckled, that's why I reacted so strongly," she says now. "I was shocked when I saw it. Why did he show up at my show? I'm not an unknown commodity. You know when you see me, it's going to be outrageous or whatever you want to call it. We tried to find him after the show and we couldn't."

She shakes her head. Did she feel bad about it? "Oh my God. I was beyond upset. The pain he must have been coming from – to take a stupid Helen Keller joke and put it all the way back to your son."

But jokes, she says, are "my whole philosophy in life, that's what keeps me going. The worst moments: if you can laugh about something you can deal with it. It shrinks it. I laughed at my mother's funeral. The hairdresser was appalled – I said to him, 'if you don't do my hair right, you'll be doing my mother's by tonight'." She laughs to herself. "But that's how I dealt with my mother's death, which I'm still not over 25 years later." At this moment, her eyes brim with tears though she recovers quickly enough.

In 1987, Rivers's husband and manager, Edgar Rosenberg, killed himself. It was the final, violent episode of a turbulent few years. In the early 80s, Rivers was one of the most successful comedians in America. She was poached from NBC, where she was Johnny Carson's guest host on The Tonight Show, by Fox, who gave her her own late-night show, but as producer Rosenberg battled with their new bosses until Rivers was fired a few months later.

With her career in freefall – for a long time Rivers was blacklisted by the US networks – and after their marriage collapsed, Rosenberg overdosed on pills. "I started laughing as soon as I could because it was so unbearable," she says quietly. "That's the way I get through things. It was horrific. Suicide is such an unnatural act and it's so out of the blue. There are no chances to say goodbye. The anger that sets in … "

Suffered depression

She is quiet for a moment. After Rosenberg's death, Rivers suffered depression, her relationship with Melissa disintegrated and she even considered suicide. "It was a terrible, horrific time. You just get through it, like you get through everything. I was making jokes." She gives a recent example: "My dog had a leg amputated and my eyes well up when I'm doing jokes about it. At the same time I'm crying."

Now, it's the deaths of good friends which fuel a lot of her coping-mechanism humour. "That's the horror of Act Three as I like to call it. You don't get to make 40-year friendships again. There's nobody to say 'do you remember … ?' That's terribly sad. Then you write jokes. People say 'he's gone to a better place'. I say 'that's impossible because he had a house in the Hamptons'."

In recent years, she hasn't been given the critical recognition that other comedians with a career spanning five decades get. Does that bother her? "I think it keeps me going," she says with a fixed smile, although in the documentary she is clearly riled by it. "They got me in a sad mood," she says. "No, I'm so lucky. I'm making a life. You always get awards right before you're going to die. I always say 'if they give you a standing ovation, they've spoken to your doctor'."

But still, without Rivers, we might not have had Kathy Griffin, Tina Fey, Sarah Silverman. Recognition comes from younger female comics, she says, but she has no time for that. "It's like you're holding on and you're hitting everyone [who is coming up] behind you, going 'Not yet!'" When they tell her she paved the way for them, it makes her angry. "I want to go, 'no, I'm paving. Look at what I'm doing now'."

Joan Rivers: A Piece of Work premiers at Sheffield Doc/Fest on 3 November and will be broadcast on More4 on 9 November at 10pm