British Prime Minister Boris Johnson and the European Union’s chief executive have given themselves until Sunday for last-ditch negotiations on a post-Brexit trade deal.

The deadline comes after the pair failed to narrow differences during a “frank discussion” over dinner in Brussels on Wednesday.

“Very large gaps remain between the two sides and it is still unclear whether these can be bridged,” according to a senior source in Johnson’s office.

He said the prime minister did not want to leave “any route to a possible deal untested” and so he and European Commission President Ursula von der Leyen had agreed to further discussions.

Von der Leyen echoed the British comments in a separate statement.

The two sides agreed that a decision on whether a deal is possible before Britain finally leaves the EU’s orbit on January 1 would be taken by the end of the weekend.

Fears are running high of a chaotic no-deal finale to the five-year Brexit crisis.

The EU and Britain had cast Thursday’s meeting as a chance to break an impasse in negotiations but both acknowledged there was a danger that a trade deal would elude them.

Britain formally left the bloc in January but has since been in a transition period during which it remains in the EU single market and customs union, meaning that rules on trade, travel and business have stayed the same.

That ends on December 31. If by then there is no agreement to protect around $US1 ($A1.3) trillion in annual trade from tariffs and quotas, businesses on both sides will suffer.

Earlier Johnson said Brussels wanted Britain to comply with new EU laws in the future or be automatically punished and was insisting it give up sovereign control over its fishing waters.

“I don’t believe those are terms any prime minister of this country should accept,” he told the British parliament, to cheers from Conservative MPs.

Johnson said “a good deal” could still be done if the EU scrapped its demands but Britain would prosper with or without a deal, a phrase he repeated as he left for Brussels.