The chairman of RBS has warned that banks could pull out of Britain unless Theresa May secures a post-Brexit transition plan.
Howard Davies said American and Japanese banks are very concerned at the prospect of a hard Brexit and are drawing up contingency plans.
He urged the Prime Minister to offer the City some reassurance and certainty by negotiating a transitional deal which will allow firms based in Britain to continue to be able to operate in the rest of the EU.
He told ITV's Peston On Sunday show that jobs could be lost to Europe and to Ireland.
He said: "I think it is damaging if we don't get a transitional deal because I think you will then see banks and financial institutions making decisions on the basis of uncertainty.
"They will not wait because they have to make a decision which will allow them to be, to continue to function in the event of a hard Brexit if that's a possibility.
"So they will not sit back, they are currently making contingency plans and once you've got a contingency plan - hey, there is a risk you might implement it one day.
"And therefore I think that it is quite urgent."
Financial firms fear they could lose membership of the single market and their passporting rights, which allow companies in the UK to operate across the European Economic Area.
Howard said the Government does not need to detail its full negotiating position, but needs to reassure the City so Britain does not encounter a "jerky and sudden" departure from the EU.
He said: "What is really important is the transitional arrangements.
"So what we are particularly focused on in the City at the moment is to try to get an understanding that actually allowing a cliff edge departure from Brexit would be damaging for everybody, because about three quarters of all European capital transactions take place in London - often by French banks or German banks etc - but they take place in London.
"If you suddenly broke that off it would be destabilising for the whole of the European financial markets.
"So what we need is a transitional arrangement, as the Article 50 process starts, so we can say 'look, here is the way in which things are going to work in the medium term'.
"In the long term, of course, I think there will be some movement of activity."
Howard said he is optimistic transitional arrangements can be drawn up as it is in the interests of the remaining EU states as well as Britain.
His warning came as Boris Johnson snubbed an emergency EU foreign ministers' meeting called to discuss Donald Trump's shock US election victory.
Foreign Secretary Mr Johnson, who branded vocal European concern about the US election result as a "whinge-o-rama", was dismissive of the need for a special EU meeting.