Tesco Bank's chief executive said on Monday that it was temporarily stopping online transactions after about 20,000 customers had money removed from their accounts after an attack by fraudsters over the weekend.
The bank, wholly owned by supermarket chain Tesco, said it had discovered there had been "significant" fraudulent criminal activity on customers' current accounts late on Saturday and early Sunday morning.
Benny Higgins, the bank's chief executive, said 40,000 of current accounts had experienced suspicious transactions and about half had money taken from their account.
He said they had now stopped online transactions until they got the situation under control, although customers could still use their cards in shops and to withdraw money from ATM machines.
"Any financial loss that results from this fraudulent activity will be borne by the bank," he told BBC radio. "Customers are not at financial risk."
He said the cost to the bank, which says it has nearly 8 million customer accounts, would be a "big number but not a huge number".
"It's 20,000 customers, we think it would it be relatively small amounts that have come out but we're still working on that," he said.