Tesco Bank, which has seen many customers unable to access their accounts last week following a technical upgrade, has said that it will consider offering compensation to affected customers on a case-by-case basis.

This comes as Tesco Bank chief executive Benny Higgins told the BBC that the bank apologised “unreservedly” for the fiasco.

Tesco strive to deliver service of the highest standard and for a significant minority of customers we have failed to do that.

“We do apologise unreservedly. It’s absolutely our focus to put this right,” Higgins told BBC Radio 4’s Money Box programme.

The bank said the technical problems that occurred when it moved 605,000 accounts from the Royal Bank of Scotland’s computer systems in-house “are resolved” for the majority of customers, but it admitted that 2,500 customers are still not able to access their accounts.

“We are working with them to resolve their issues through email and on the phone,” a spokesperson for the bank said.

Last Thursday, Tesco Bank was forced to issue urgent guidance on how to make a popular browser, Microsoft Internet Explorer 9, work on its website.

However, a Computerworld UK reader indicated that the problems were clearly not resolved by the weekend.

“Now 5 days and still no access to my money – I’ve been on the phone for hours but only get a recorded message,” Rp Easterbrook2  commented.

The reader’s comment highlighted an issue experienced by many customers, of not being able to get through to Tesco Bank’s customer service phone lines without a long wait, despite the bank increasing the number of call centre operatives.

Nonetheless, another reader emailed to say that after an hour-long wait, he was able to sort out the issues.

“After waiting for 60 minutes for the call to the customer services to be answered they were very helpful in sorting out all the problems. A lot of the problems were caused by Tesco not properly testing the system and not describing various steps in plain English,” said David Taylor.