Chancellor Philip Hammond has told European leaders that it is in the "mutual interest" of both the UK and the EU to include financial services in a free trade agreement.
In a speech, Mr Hammond set out his argument against "sceptics", saying it is possible to reach a deal.
But EU president Donald Tusk flat out rejected the UK proposals.
The EU's chief Brexit negotiator, Michel Barnier, has argued that such a deal had never been done before.
But Mr Hammond said the EU has in the past attempted similar agreements.
In December, Mr Barnier said: "There is not a single trade agreement that is open to financial services. It doesn't exist."
Mr Hammond said on Wednesday that the EU itself tried to include financial services on trade deals with the US and Canada.
He said: "If it could be done with Canada or the USA... it could be done with the UK."
The Chancellor stressed: "I am clear not only that it is possible to include financial services within a trade deal but that it is very much in our mutual interest to do so."
However, European Union president Donald Tusk issued guidelines on Wednesday telling EU negotiators that the UK will have to settle for a more conventional free trade agreement, such as the EU's deal with Canada.
The UK's stance on leaving the single market means the City having to settle for more limited access to European markets, he said.
"I fully understand and of course I respect Theresa May's [political] objective - to demonstrate at any price that Brexit could be a success and was the right choice.
"But sorry, that is not our objective," Mr Tusk added.
The EU's chief Brexit negotiator Michel Barnier says a trade deal including financial services "does not exist".
Mr Hammond said: "The EU is a very skilled negotiator... they've negotiated agreements with many countries. They are very skilled and very disciplined in the way they carry out their negotiation, and it doesn't surprise me remotely that what they've set out this morning is a very tough position.
"That's what any competent, skilled and experienced negotiator would do. I expect that we will have a deep and constructive engagement with them, and I hope that what I've set out here this afternoon will contribute to the discussion that we'll be having."
On Tuesday, French economy minister Bruno Le Maire told the BBC: "Financial services cannot be in a free trade agreement, for many reasons, for reasons of stability, for the sake of supervision because there are some very specific rules for financial services."
He said that the "best solution", would be for a system of "equivalence" where both sides recognised each other's standards.
But Mr Hammond said: "It is time to address the sceptics who say a trade deal including financial services cannot be done because it has never been done before.
"To them I say 'every trade deal the EU has ever done has been unique'.
"The EU has never negotiated the same arrangement twice. It has bespoke relationships with Turkey, Canada, Singapore, South Korea, Switzerland."
Analysis: Kamal Ahmed, economics editor
In his speech on UK-EU co-operation post-Brexit, the Chancellor referred to past attempts at forging a free trade agreement between the US and Europe.
"The EU itself pursued ambitious financial services co-operation in its proposals for TTIP [the now aborted Trans-Atlantic Trade and Investment Partnership]," Mr Hammond said.
"Which it described as a partnership that would be: 'more than a traditional free trade agreement'."
Mr Hammond argued that if the EU tried it before with a nation which doesn't have regulatory alignment on financial services - America - then surely it can do so with a country that it at present does - the UK.
But the Chancellor also said a lot more than that.
Because the person who proposed "regulatory co-operation" on financial services as part of the EU-US free trade negotiations was one Michel Barnier.
Shadow Chancellor John McDonnell said: "The Chancellor has shown his hand, and it is clear he is looking for a TTIP type deal as his blueprint.
"Yet those negotiations took nearly four years and collapsed, which is why a transition period is critical."
Mr Hammond also said: "A trade deal between the UK and the EU must start from the reality of today, that our economies, including in financial services, are interconnected, that our regulatory frameworks are identical."
Stephen Jones, chief executive of UK Finance, the trade body that represents the UK financial services sector, said: "Thousands of customers and businesses in Europe rely on access to financial services from the UK. It is in everyone's interests for this vital cross-border trade to continue."