HSBC says its online banking services are now stable, following two days of disruption earlier this week.
Throughout Monday and most of Tuesday, the personal banking site was not allowing customers to log on, while business accounts were running slowly.
On Wednesday morning, it said some customers might still be experiencing "intermittent issues" while trying to get online.
Nevertheless, it said "final fixes" were being put in place.
The bank, which has 17 million customers, has still not given a precise explanation as to what went wrong.
It blamed the problem on a complex technical issue within its banking and mobile systems.
Twitter post from HSBCImage copyrightTwitter
HSBC apologised and promised that no customers would lose out financially as a result of going into the red or not being able to make payments.
The chair of the Treasury Select Committee, Andrew Tyrie, promised to grill HSBC's chief executive on why such failures keep occurring.
HSBC was hit by a previous IT glitch in August 2015, which prevented 275,000 payments going through just ahead of the Bank Holiday weekend.
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