David Davis has appeared to cut the odds on a “no deal” Brexit by insisting Britain will only agree to a transition phase if the “final relationship” has been agreed.

The Brexit Secretary vowed Britain would not sign up to what one Conservative MP called a “permanent bridge to nowhere”, where no future trading agreement has been reached.

The stance raises the likelihood that Britain will crash out of the EU with no deal – because key figures at home and abroad have insisted there is no time to agree permanent trading terms.

It was immediately criticised as “an extraordinarily dangerous statement” which hiked the risk of “the most destructive possible option for our economy”.

Ian Murray, a Labour MP and supporter of the Open Britain group, added: “Neither the Governor of the Bank of England, nor anyone credible in business, believes it is likely that the final deal on Britain’s future relationship with Europe can be fully negotiated by 2019.

“David Davis needs to engage with the real world, and stop living in a fantasy land where these negotiations are going swimmingly.”

The Liberal Democrat Brexit spokesman, Tom Brake, said: “The Brexit Secretary is living in fantasy land.

“There's no way the government can negotiate a final deal in time with the EU when Cabinet ministers can’t even agree amongst themselves. David Davis is either sneakily pushing us towards a no-deal, or has no idea what he’s doing.”

The controversy came as the EU’s chief negotiator, speaking in Brussels, made clear the exit talks will remain deadlocked without further concessions from London.

Blaming Britain for the stalemate, Michel Barnier said “it takes two to accelerate”, adding: “It is very important to understand that time passes very quickly. The clock is ticking very fast.”

In her Florence speech, Theresa May proposed a transition of “about two years”, to calm the fears of businesses, a move warmly welcomed in Brussels.

She has described it as an "implementation period" - to put into place agreed arrangements, rather than delay a long-term agreement - but had avoided setting down further conditions.

The move recognised widespread warnings that a final deal is likely to take many years to agree, with the risk of a “cliff edge” in March 2019, the Prime Minister has acknowledged.

But Mr Davis toughened that position in a statement to MPs in which he also admitted the EU was using the weapon of “time pressure” to turn the screw on Britain in the negotiations.

Rishi Sunak, a Brexit-backing Tory backbencher, urged him to only accept transition “if the final relationship with our European allies has been agreed, at least in principle”.

The Government must ensure that “what is meant to be a transitory state of affairs does not become a permanent bridge to nowhere”, he said

In reply, Mr Davis said: “He is right. Such a transition phase would only be triggered once we have completed the deal itself.

“We cannot carry on negotiating through that. Our negotiating position during the transition phase would not be very strong.”

The Brexit Secretary has previously argued Britain holds the whip hand in the talks, but admitted: “They are using time pressure to get more money out of us.”

The comment reflects that one quarter of the two-year Article 50 process has already ticked away. The EU says a deal is needed in 12 months, to allow for ratification.

Mr Davis also dismissed any shift in the British position on a future Irish border – attacked as “fantasy” in Brussels – arguing: “We have made quite a lot progress on Northern Ireland, possibly as much as we can.”