Lloyds, Halifax and Bank of Scotland customers were unable to use online banking for hours on New Year's Day.
Mobile banking through the smartphone apps was also unavailable for most people.
All three banks, which are part of Lloyds Banking Group, tweeted to say the services were back to normal at around 1.30pm, after apologising to customers and saying they were working to fix the problems.
The message said: "Internet and Mobile banking is now back to normal. We're sorry for the issues with it this morning. Thanks for your messages."
The Down Detector website reported that thousands of users were unable to access online and mobile banking from around 4am.
Customers also complained on social media.
One said: "Will online banking be back up for tomorrow? It’s direct debits day for most people tomorrow and how can they know what’s going on on their accounts if they can’t see it?"
Some joked that the so-called Millennium Bug - also called the Y2K Bug - had hit 20 years late.
Several Twitter users complained about being unable to log in to their banking apps while others asked when they might be up and running again.
One asked: "@Lloydsbank will online banking be back up for tomorrow? It’s direct debits day for most people tomorrow and how can they know what’s going on on their accounts if they can’t see it??"
Another said: "@HalifaxBank if I don’t pay my rent and other bills today I will be charged late payments... can you explain how this can be resolved?!"
