The latest banking glitches arose on what is pay day for many people, being the last Friday of the month.
HSBC said on Friday morning that its service was recovering, with the first issues reported at around 7.45am.
An HSBC UK spokesman said: “We are aware there are still intermittent issues accessing HSBC UK mobile banking services.
“Services are recovering, but if a customer continues to experience problems they should continue to retry or our online banking services are available via browser. We apologise for any inconvenience caused.”
TSB’s problems started at around 8am - and it said internet banking was affected as well as the app.
A TSB spokeswoman said: “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.
“Customers are still able to use their cards as normal.”
The problems come after customers of NatWest, Ulster Bank, Royal Bank of Scotland and Barclays struggled to log in last week.
The banking problems also follow TSB’s huge IT meltdown earlier this year, after a botched IT switch saw millions of customers locked out of accounts.
Fed-up customers expressed their annoyance on Twitter at the latest disruption.
One user told TSB: “Yet again I can’t access any of my accounts. How many times???”
Another said: “Again. And again. And again. Why does your app keep crashing? All I want to do is check my account!”
And another told TSB: “This might just be the thing that finally makes me change bank.”