(Adds Tusk's press conference)
BRUSSELS, March 7 (Reuters) - The European Union on Wednesday offered Britain a free trade agreement for their post-Brexit relationship that fell well short of ambitions set out by Prime Minister Theresa May last week, notably for the key financial sector.
A draft position of the remaining 27 EU members said the bloc was determined to foster a close partnership with Britain, but its depth would be limited by Britain's own wish to leave the EU's single market and customs union.
"Because of Brexit, we will be drifting apart," the chairman of EU leaders Donald Tusk told a news conference, delivering a message that contrasted sharply with May's call for future trade to be "frictionless as possible".
"In fact, this will be the first free-trade agreement in history that loosens economic ties instead of strengthening them. Our agreement will not make trade between the UK and the EU frictionless or smoother. It will make it more complicated and costly than today for all of us," he said.
Crucially, the bloc said Britain would be treated like any other third country when it came to financial services - which London had pressed to be included in a future free-trade deal.
Financial services generate more than 10 percent of Britain's output and are the only area in which Britain has a trade surplus with the EU, making London very keen to preserve its banks' current access to continental Europe.
But the text said in the future, Britain's financial firms would only be allowed to operate in the EU "under host state rules" and be treated according to "the fact that the UK will become a third country and the Union and the UK will no longer share a common regulatory, supervisory, enforcement and judiciary framework."
LIMITED ACCESS FOR BANKS
British finance minister Philip Hammond will say later on Wednesday that the EU must drop its tough stance and allow Britain's giant financial services sector to be part of a post-Brexit trade deal, according to speech extracts.
Hammond will argue that Brussels originally aimed to include financial services in a free trade deal with Canada which in the end failed to provide much new access for banks. The EU had also wanted to include the sector in now-stalled trade talks with the United States.
In the end, the "CETA" EU-Canada trade deal has only a minimal section on financial services. If a Canadian financial firm wants to do business in the EU it must set up a presence inside the bloc and comply with EU regulations.
The draft EU guidelines, which will be worked on by EU diplomats to be approved by the bloc's 27 national leaders in late March, say services will indeed be part of the deal, but spell out clear limits of what can be on offer.
"Such an agreement cannot offer the same benefits as Membership and cannot amount to participation in the Single Market or parts thereof," the text read.
"Like other free trade agreements, it (the trade agreement) should address services," Tusk said. "(But) No Member State is free to pick only those sectors of the Single Market it likes, nor to accept the role of the ECJ only when it suits their interest," he said.
"By the same token, a pick-and-mix approach for a non-member state is out of the question. We are not going to sacrifice these principles. It's simply not in our interest," he said.
Last December the Bank of England proposed allowing EU banks in Britain to continue as branches in London after Brexit on condition of some form of reciprocity from Brussels to avoid lenders having to find extra capital to become fully fledged subsidiaries.
Instead, the EU proposal sticks with the bloc's traditional approach to dealing with banks from non-EU or third countries.
"This means double regulation. You operate in London under UK rules and some elements would be under their rules for cross-border services," Barney Reynolds, a partner at law firm Shearman & Sterling said. (Additional reporting by Alissa de Carbonnel, Philip Blenkinsop, Huw Jones, Writing by Gabriela Baczynska; editing by Mark John)