After more than five days of being locked out of their online bank, TSB customers can now access their accounts.
But the bank has limited the number of people who can get into their accounts at any one time, because it expects a surge in customers trying to use it.
The bank’s upgrade to its banking systems has been causing chaos for customers since the weekend.
On Tuesday, chief executive Paul Pester said he was “deeply sorry”.
No one would be left out of pocket, he added.
Early on Wednesday morning, he tweeted: “Our mobile banking app and online banking are now up and running. Thank you for your patience and for bearing with us.”
The bank had hoped to restore services on Tuesday afternoon, having taken down its mobile app and online banking “for a few hours” earlier in the day after it received a huge backlash from annoyed customers.
However, delays ensued because of the large volumes of people wanting to use it after the scheduled downtime.
TSB warned its users that it was carrying out upgrades at the weekend between 16:00 on Friday and 18:00 on Sunday.
But a number of customers reported problems long after the scheduled restart time, with many worried about being able to pay bills or even get cash to pay for essentials.
On Wednesday morning, some hours after the system had been back up and running for the second time, Martin Skipworth told the BBC: “I actually managed to log in to TSB internet banking this morning, but once in, it is so slow and when you switch pages, it just hangs.
“I have tried again and can’t access anything now, It’s a complete shambles.”
Others took to Twitter to express their anger or worry about charges.
Apart from rage at being unable to get at their money, on Sunday some customers reported being able to see other customers’ details in a suspected data breach that is being looked into by the Information Commissioner’s Office.
Nicky Morgan MP, chair of the Treasury Committee, called for the bank to explain how it intended to compensate the customers who suffered a breach of potentially highly-sensitive personal data.
Meanwhile, the City watchdog said it was “working with the firm to ensure customers are properly communicated with and are not left out of pocket”.
The Financial Conduct Authority added: “”We will be talking to the firm to understand exactly what went wrong and the steps that they are taking to ensure something like this does not happen again.”