TSB customers are still unable to make payments or access key accounts almost a month after the botched IT upgrade.

As one group of analysts said the chaos could cost TSB as much as £56m this year alone, many of the problems that have bedeviled the bank are yet to be resolved as the crisis enters its fifth week.

TSB mortgage account holders are still unable to access accounts online, while business customers continue to face problems making online payments.

Some credit card customers are still being wrongly told that payment of £0.00 will be taken, while the bank’s internal secure messaging service remains unavailable.

Personal customers have been furious at the bank’s lack of response after they had their accounts cleared out by fraudsters. One said he was only refunded after he spent three days camped in his local branch. Another, whose mother had died, said he was forced to drive from London to Wimborne in Dorset to inform her local bank branch, as it was impossible to get through on the phone.

At the beginning of May, TSB’s chief executive Paul Pester told MPs that the bank would have things back to normal “soon”. However, it is clear that the problems have proved harder to fix than previously thought.

Pester told the Treasury select committee the bank had received 40,000 complaints about the outage. He was accused of complacency for saying the migration had mostly gone smoothly, and not knowing exactly how many of the bank’s 1.9 million online customers had been affected.

Customers began experiencing problems with their accounts on Sunday 22 April after the bank – owned by Spanish lender Sabadell – migrated from an IT system inherited from the previous owner, Lloyds Banking Group. Sabadell had hoped to make more than £100m in annual savings by using the new system.

However, it now look set to lose most of that in fines and other payments.

Analysts at Royal Bank of Canada said last week that the group faced fines of an estimated £16m from UK financial regulators.

Following Royal Bank of Scotland’s June 2012 IT meltdown that left some people locked out of their accounts for days on end, the much bigger RBS paid fines of £56m.

The Canadian bank said TSB’s offer to hike the interest rate on its Classic plus account to 5% will have cost £22m by the end of this year. The decision to waive overdraft and other interest charges for two months will set it back £18m, giving a £56m hit this year.

TSB disputes RBC’s calculations, though, and says it is working around the clock to fix the problems.

“We’re aware that RBC has agreed to reissue its report, as the basis for the conclusions was clearly misleading and based on a tiny fraction of customers. Our focus is putting things right for our customers – and no customer will be out of pocket as a result of what’s happened,” a TSB spokeswoman said.