The TSB chief executive was forced to admit on Wednesday that problems persisted with the firm’s mobile and online banking for a sixth day – after confidently declaring only hours earlier that services were back up and running.

TSB said internet banking was operating at 50% of capacity, which means that for every 10 customers only five will be able to access this service. Mobile banking was operating at around 90% of capacity, the bank said in a statement issued at about 4pm.

Paul Pester, the TSB chief executive, said the bank’s teams were working “around the clock to fix the problems that some of our customers are having in accessing their TSB accounts”.

He said the engine room of the bank was working as it should. “This means that for the vast majority of our five million customers everything is running smoothly.”

He said direct debits, standing orders, payments including salary credits and transfers going in and out of accounts were working as normal.

“The challenge we are facing at the moment is that while we know everything is working, one of the main ways that our customers see everything is working – through our internet banking and mobile app – isn’t functioning as well as it should be, and for this I’m truly sorry,” he added. “I can appreciate how frustrating this must be for our customers.”

He reiterated that no one would be left out of pocket.

Regulatory scrutiny of the IT crisis, one of the biggest for years in Britain’s banking sector, has intensified. The Financial Conduct Authority said it had a small team in place at TSB, “assessing the situation”.

As the crisis rumbled on, a number of TSB’s 1.9 million mobile and internet customers continued to vent their anger on social media. Some said that although they could access the TSB app, their mortgages seemed to have disappeared.

Stacey Kavanagh was one of several who complained on Twitter that her mortgage had vanished. “The incompetence of TSB continues; the app now works, but it would appear that I no longer have a mortgage. I assume that means you won’t be taking any money from me on payday?” she asked.

Pester had suggested in a tweet early on Wednesday that problems with the botched IT migration were solved.

Some customers who had been locked out of their accounts for days were still unable to get into them on Wednesday, as TSB limited access to internet and mobile banking in an attempt to manage the scale of traffic.

A spokesperson for TSB said customers who were having trouble accessing the mobile app should shut it down completely and then reload.

The bank is facing a potential multimillion-pound compensation bill and regulatory fines for the crisis, which began on Friday night when TSB started a long-planned move of 1.3bn customer records from its former parent company, Lloyds Banking Group, to a platform built by TSB’s Spanish owner, Banco Sabadell. Customers had been told the transfer would be completed by 6pm on Sunday.

Small businesses were unable to pay salaries or manage transactions, while some account holders found all their direct debits had disappeared and others reported that their cards were declined when shopping.

Multimillion-pound bonuses to the chief executive and 30 other senior TSB staff were linked to the IT overhaul and are now under threat. The payouts include a potential £1.6m bonus for Pester. They were frozen after TSB was forced to delay the move from Lloyds to Sabadell last year.