British Bankers' Association chief Anthony Browne's dramatic claim was made in an article published today in the 'Observer' newspaper. Browne said smaller banks could also move operations overseas by next year.
"Their hands are quivering over the relocate button. Many smaller banks plan to start relocations before Christmas; bigger banks are expected to start in the first quarter of next year," he wrote.
"It is the UK's biggest export industry by far and is more internationally mobile than most. But it also gets its rules and legal rights to serve its customers cross-border from the EU.
"For banks, Brexit does not simply mean additional tariffs being imposed on trade - as is likely to be the case with other sectors. It is about whether banks have the legal right to provide services."
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Banks, which had overwhelming campaigned for Britain to remain in the European Union (EU) in the June 23 referendum, want to see the continuation of the EU's "passporting" system, allowing UK-based financial services to operate across Europe without needing separate authorisation.
"The problem comes - as seems increasingly likely, judging by the rhetoric - when national governments try to use the EU exit negotiations to build walls across the Channel to split Europe's integrated financial market in two, in order to force jobs from London," Browne says.
"From a European perspective, this would be cutting off its nose to spite its face. It might lead to a few jobs moving to Paris or Frankfurt but it will make it more expensive for companies in France and Germany to raise money for investment, slowing the wider economy," he adds.
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