The BBA is the main trade association for the UK banking sector with 200 member banks.
BBA chief Anthony Browne gave the warning in an opinion piece in Sunday's Observer newspaper. Here is the key section (emphasis ours):
"But businesses can't wait to the last minute. It takes years to move operations. Banks might hope for the best but have to plan for the worst. Most international banks now have project teams working out which operations they need to move to ensure they can continue serving customers, the date by which this must happen and how best to do it. 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."
Browne's comments are the most stark warnings to be said yet that London's financial status could be seriously diminished by Brexit.
JPMorgan and UBS have already publicly stated that they may have to move thousands of jobs out of the UK as a result of Brexit and Goldman Sachs is said to be considering moving up to 2,000 roles from Britain to the EU.
A confidential Deutsche Bank briefing document obtained by Business Insider predicted that top banks would look to move out of Britain to elsewhere in Europe as a result of the June 23 Brexit vote.
The key issue is passporting rights. Banks currently have the right to "passport" their financial licences in one EU market to another, preventing them having to go through the costly and complicated process of being regulated in each market where they operate.
The Financial Conduct Authority (FCA) said earlier this year that 5,500 UK companies rely on passporting rights, with a combined turnover of £9 billion.
It is looking increasingly likely that Britain will lose its passporting rights, with the government making it increasingly clear that it will prioritise control over immigration in Brexit debates. European officials have repeatedly signalled that passporting rights are tied to access to the single market and Britain will have to forego the financial rights if it wants to regain control over its borders.
The BBA's Browne says that "the public and political debate is taking us in the wrong direction," and says he fears that Europe will "be cutting off its nose to spite its face," by erecting trade barriers with the UK to punish it for Brexit. He says the trade in financial services between Britain and continental Europe is worth £20 billion a year, Browne says.
The idea of Britain relying on "equivalence" rights, where the EU allows licences deemed similar to its own to be used across the area, has been suggested by some negotiators. But Browne says: "For most banks, having equivalence won't prevent banks from relocating their operations."