The EU has dashed the government's hopes of carving out a special arrangement to allow City firms to trade freely in the EU if Britain leaves the single market.
Michel Barnier, the European Commission's chief Brexit negotiator, said he was not open to a free trade agreement including financial services.
"There is no place (for financial services)," he said. "There is not a single trade agreement that is open to financial services. It doesn't exist."
Describing the position as a result of "the red lines that the British have chosen themselves", he stated: "In leaving the single market, they lose the financial services passport."
Barnier's warning came on the eve of the first full Cabinet discussion of the "end state" which the UK is aiming for in upcoming negotiations on Britain's future relationship with the EU.
He said that the UK must follow all EU rules during the expected two-year transition period following the official date of Brexit in March 2019 - including laws introduced during that time with no British input into decisions.
And while Britain can negotiate trade deals with other countries during the transition, they cannot enter into force until the period is over, probably in 2021.
Barnier said he believed that a UK/EU free trade deal could be agreed within the two-year transition, but said it would have to be ratified by more than 35 national and regional parliaments across the EU27, each of which holds a veto.
He also insisted that the UK must accept the "complete architecture" of the EU - including the role of the European Court of Justice, free movement of people and the CFP - during the transition, saying: "It will be essentially the economic status quo."
May has repeatedly made clear that she intends to take Britain out of the single market and customs union after Brexit, effectively ruling out Norway-style free access to trade with the EU27.
But she has suggested that a "deep and special partnership" with the remaining EU should be more extensive than the agreement struck with Canada in 2016, which covers goods but not services.
Brexit Secretary David Davis has called for a "Canada plus plus plus" deal which would include financial services.
Members of May's "Brexit war cabinet" of senior ministers heard her say on Monday that she would "aim high" in negotiations for the post-Brexit trade deal.
But no agreement was reached on the shape of the deal which the UK should seek, with convinced Brexiteers like Boris Johnson, Michael Gove and Liam Fox - alongside Gavin Williamson, who voted Remain in the referendum - arguing for a clean break which will allow Britain to diverge from EU regulations as it forges new trade deals elsewhere in the world.
Meanwhile others including Philip Hammond and Amber Rudd pressed the case for continued regulatory "alignment" to maximise access to EU markets.
There was discussion of the potential for "gradual divergence" - a step-by-step move away from EU laws after Brexit and the conclusion of a subsequent implementation period in 2021.
The "end state" will also be discussed in full Cabinet on Tuesday, but insiders suggested there would be several more meetings before a formal Government position is finalised in the early weeks of the new year.
Barnier made clear that the EU will respond firmly to any deviation from the framework of single market regulations which might give the UK a competitive advantage through lower taxes or weaker standards.
"We will not accept from the other side, regulatory competition against social rights, against environmental rights, against consumer rights and against fiscal regulations ... or against financial stability," he said.
And in reference to US pressure on the UK to ditch EU food standards in the hope of securing a free trade deal, he said: "We will not accept chlorinated chickens, nor other products that do not meet our food standards."
In response to Barnier's comments, Liberal Democrat Brexit spokesman Tom Brake said: "We are now starting to see the real potential costs to ripping up our trade deal with Europe."
But the co-chairmen of the Leave Means Leave group wrote an open letter to the Cabinet, urging them to break with EU red tape.
"The proposed regulatory alignment is completely unacceptable and incompatible with the vision of Britain leaving the EU," wrote Richard Tice and John Longworth.