Customers of the two banks reported the issues on Twitter, before both lenders provided further updates.
A TSB spokesperson told Mortgage Solutions that the services have now been fixed – a similar problem happened earlier this month at the bank.
And at the beginning of this month TSB chief executive Paul Pester stepped down due to the bank’s IT failures.
In April, customers were locked out of their accounts for weeks following a botched systems upgrade.
A TSB spokesperson said: “We’re sorry for any issues our customers experienced this morning on our mobile app and internet banking. These services are now recovering back to normal levels so please retry if you have experienced issues.
“Our cards, branch and telephone services continue to operate as normal.”
HSBC customers have also experienced problems today.
However, a spokesman from HSBC told Mortgage Solutions services are recovering and the majority of customers are now able to log-on to their mobile banking app.
He said: “However, we are continuing to monitor the issue. 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.”
Many customers complained on Twitter about the poor mobile and online performances.