Santander UK customers were unable to access their online accounts for several hours from Friday morning until mid-afternoon.
"We are currently experiencing issues with customers logging in to Online Banking," the lender told customers via Twitter.
It comes ahead of a bank holiday weekend and monthly salary payments for millions of Britons.
The bank said the problem had now been sorted out.
"We apologise for the problems some customers faced earlier today using our digital banking services," the lender said in a statement. "These have now been fixed and we can confirm that any payments due today will have been processed."
It said debit cards, credit cards and cash machines should all have been working during the outage.
While outages that last less than a day will be a minor nuisance to most customers, there could be significant knock-on problems for those planning on large transfers ahead of big purchases, such as for a car or home.
Sophie Rivett, from Worcester, told the PA news agency she had problems paying her bills as she moved into a new house on Friday.
She said: "I am in the middle of moving house, had to borrow money from family."
Some frustrated customers left comments on the website Downdetector, which monitors IT issues on different services.
"Phew. Just got in and paid two bills. Oh, the relief", said one user after it was reported the problem had been resolved.
"But really - not good enough, Santander...you don't muck about with stuff at the end of the month. How about some compensation for your frustrated customers?"