The Financial Services Authority said the great majority of financial groups were on course to beat the "Y2K" problem. Of 160 "high-impact groups" - those with a big customer base or a crucial role in the financial system - 148 were on track or likely to be on track by the end of the year.
But 12 of the companies - 8 per cent of the total - presented a "serious risk" and were marked "red" under the FSA's traffic light grading system for Y2K compliance. A further 56 big firms were behind schedule but likely to get on track.
Speaking at an FSA-organised conference, Michael Foot, head of banking supervision at the FSA, did not name the firms or their business. But he said they were all foreign-owned and were either insurance companies, banks or investment houses. Most were household names.
Mr Foot held out the prospect of withdrawing authorisation from the firms concerned, effectively forcing them to close down or sell out to a rival.
"We could, for example, say to a firm: `We are going to have to take your authorisation away.' That could happen if the costs are so great that the customers' interests would be better served by the firm being shut down."
So far the conditions that would cause the FSA to shut a firm down did not obtain, he said. Moderate solutions - such as shutting down a particular line of business - were more likely.
Mr Foot said the firms placed on "red" were unlikely to agree with its judgement. "It's a sort of `It'll be all right on the night' attitude," he said. The firms will be challenged to prove the FSA wrong or find a convincing way around the problem.
Bankers said they were making shortlists of banks they knew would be safe to deal with.