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Speaking to the BBC at the World Economic Forum in Davos, Mr Dimon said: "If we can't find reciprocal recognition of rules - and there are a lot of people who are mad with the Brits for leaving and want their pound of flesh - then it could be bad. It could be more than 4,000.”
JP Morgan warned in the run-up to the referendum that 4,000 jobs could go if the UK voted to leave the EU but had recently played down that figure, instead estimating that between 500 and 1,000 roles could move.
But Mr Dimon said a lack of agreement on financial services cross-border trade could seriously damage London’s status as a global financial hub over the long term.
Goldman Sachs boss Lloyd Blankfein later told the BBC in Davos that some steps taken by the Wall Street bank to prepare for Brexit were "not going to be undone".
"Once we start to repaper - which is very cumbersome because it involves lots of lawyers on both sides and takes months - once we start that are we going to go back? Probably not," he said.
One of the most powerful bankers in the world, Mr Blankfein has been publicly airing his Brexit concerns and support for Frankfurt and Paris on Twitter in recent months. The bank has already taken out ten floors in a new building in Frankfurt in preparation for March 2019.
Financial firms in the City are getting increasingly jittery about the lack of progress in Brexit trade talks.
Swiss investment bank UBS - which employs 5,000 people in London - told investors earlier this week it planned to implement its Brexit contingency plans early this year. [...]