More than 16,000 customers have deserted the TSB in the wake of an IT meltdown earlier this year.
The figures – released by the payments operator BACS – show the net loss in accounts between April and June.
As many as 1.9 million people were left unable to access their own money in April, after the bank tried to introduce a new computer system.
The crisis resulted in the resignation of the bank’s chief executive and an enquiry by the regulator.
The Financial Conduct Authority (FCA) is still considering whether to fine the bank, after it was judged to have misled Parliament over the issue.
The number of customers switching their accounts elsewhere is likely to be exacerbated by further computer problems experienced by the TSB in September.
“As expected, customers voted with their feet on the back of the TSB IT fiasco, with the bank losing a net 16,641 customers to rivals,” said Andrew Hagger of Moneycomms.co.uk.
“The only real surprise is that this figure wasn’t much higher – although the discontent could rumble on and we may yet see a similar outflow of accounts when the next quarterly figures are released next January.”
The Royal Bank of Scotland (RBS) was the next biggest loser in the quarter, with 12,362 customers switching to accounts elsewhere.
The biggest gainers were the Nationwide Building Society, which attracted an extra 34,577 customers, and HSBC which gained 25,605.