TSB and HSBC have become the latest banks to be hit by computer glitches.
TSB said users of its smartphone app and internet banking were having difficulty logging in.
HSBC said about 50% of mobile users were having trouble connecting, although many succeeded when they tried a second time.
It is the latest in a string of IT outages for the industry, including the recent high-profile meltdown at TSB.
TSB said in a tweet: “We’re aware of an issue affecting some of our customers when they are using our mobile app and Internet Banking this morning. We are working hard to fix these issues and will update again as soon as we can.”
HSBC tweeted: “We are aware some customers are experiencing problems using Mobile Banking. We are investigating and will provide further updates. If your query is urgent please call us on 03 457 404 404. We are sorry for any inconvenience caused.”
On Twitter, HSBC customers began posting reports of being locked out of the app from about 07:30.
Last week, RBS, NatWest and Ulster Bank reported problems with customers unable to access their bank accounts online. Customers were locked out for about five hours.
Earlier this year, TSB’s huge IT meltdown led to weeks of pain for customers and the eventual resignation of chief executive Paul Pester.