Brussels has been accused of “wishful thinking” over claims that the UK could be prepared to compromise on fishing and demands for alignment with European Union standards.

Downing Street accused the EU of failing to acknowledge the reality of the UK’s status as an independent country as a fourth round of talks on a post-Brexit trade deal got under way.

The teams led by Boris Johnson’s Europe adviser David Frost and the EU’s negotiator Michel Barnier are meeting virtually for the latest round of discussions after previous sessions were described as “tetchy” and failed to make a breakthrough.

Progress needs to be made ahead of a high-level summit later this month between Mr Johnson and EU chief Ursula von der Leyen.

The UK has already indicated it will walk away from the negotiations if there is no prospect of an agreement by the time of the summit.

A Times report suggested the UK would be willing to compromise on fisheries and the “level playing field” trade rules if the European Union agrees to back away from its “maximalist” demands related to regulatory alignment and fishing access.

“There is only one way to get things moving and that is for the UK side to move and then, as Frost knows full well, the EU will move too,” a senior diplomatic source told the newspaper.

But the Prime Minister’s official spokesman said: “This is wishful thinking by the EU.

“We have always been clear there is no question of splitting the difference on level playing field and fish.

“We are not compromising on those because our position on these is fundamental to an independent country.

“Any agreement has to deal with this reality.”

The spokesman said there had to be a “balanced solution” which reflects the “political reality” on both sides.

“What we cannot do is agree to any EU demands for us to give up our rights as an independent state.”

Mr Barnier said it was a “crucial week” to make “tangible progress” across all areas of the talks.

Meanwhile, industry leaders said any attempt by the EU to withhold a post-Brexit trade deal over fishing rights would be a “nuclear option”.

Barrie Deas, chief executive of the National Federation of Fishermen’s Organisations, said he did not believe “capitulation” by the British was likely.

He said the EU had taken a “hard line” and there was not much optimism a deal on fishing could be reached by the end of June, which is the aim of the Withdrawal Agreement.

But as European fishing vessels fish six times as much in UK waters as British vessels do in EU waters, the UK has leverage in the talks, Mr Deas said.

He said: “Fishing rights are an entirely separate issue, the EU are trying to link them because it’s the only card they believe they have.

“It’s a nuclear option and would be extremely damaging to the EU as well as to the UK, that’s why I think there will be a compromise at some stage because it’s in the parties’ interests.”

A compromise could be based on EU fleets being assured they could fish in UK waters but not on the same quota shares as before, Mr Deas said.