The EU’s Brexit negotiator Michel Barnier said he was very happy to be back in London on Sunday and work would continue on a trade deal with Britain.
The chief negotiators, Mr Barnier and Britain's David Frost, will resume talks in London on Monday to "redouble efforts to reach a deal", Downing Street said earlier.
British Prime Minister Boris Johnson had earlier said a trade deal with the bloc was "there to be done".
After months of talks on a deal to protect trade from quotas and tariffs, the two sides have yet to close significant differences on at least two main sticking points.
Disagreements on guarantees for fair competition, especially over state aid rules and fisheries, have dogged the talks since Britain left the EU in January.
Both sides have called on the other to compromise to unlock an agreement in increasingly testy exchanges that have underlined a lack of trust, especially after Britain moved to undermine parts of an earlier divorce deal.
Any deal should be agreed on by mid-November to allow for ratification, with some businesses hoping that the time pressure and the pandemic resurging across much of Europe can focus minds to avoid disruption at the end of the year.
The Brexit transition period is due to end on December 31, after which the two parties will trade on World Trade Organisation terms, bringing in tariffs on many goods, if a deal were not reached.
"I've always been a great enthusiast for a trade deal with our European friends and partners," Mr Johnson said.
"The broad outlines are pretty clear. We just need to get on and do it if we can.
"I said that to [European Commission President] Ursula von der Leyen just yesterday. And she totally agrees with me."
Earlier, UK Foreign Minister Dominic Raab told the BBC that there was "a good chance of a deal if we get the flexibility from the EU on fisheries and a level playing field".
Britain wants a separate trade deal with the US, but some say Mr Johnson might struggle to form close ties with President-elect Joe Biden.
Mr Biden has in the past cast doubt over Brexit and has never met Mr Johnson.