British Prime Minister Boris Johnson has told his cabinet a last-minute deal is still possible, as the two sides pressed on with intensive talks to try to avoid a disorderly Brexit on October 31, the date set for Britain's departure.

"The prime minister said there was a way forward for a deal that could secure all our interests ... but that there is still a significant amount of work to get there and we must remain prepared to leave (without a deal) on October 31," a spokeswoman from Johnson's office said on Sunday.

Britain said the latest talks had been "constructive" and there would be more talks on Monday.

Johnson hopes a deal will be agreed in time for EU leaders to approve it at a summit in Brussels on Thursday and Friday.

But he would still have to convince a deeply divided British parliament to ratify the agreement, probably at a rare Saturday session on October 19.

The European Commission, the EU's executive, said talks would continue on Monday and EU negotiator Michel Barnier would update the 27 member states - all except Britain - at a meeting in Luxembourg on Tuesday.

An EU diplomat said there were still differences on the customs issue.

"Small chances (remain) that a text could be ready for the summit and we won't negotiate at the summit," the diplomat said.

"If talks are going well, we might say there is progress but more time is needed to continue."

A delay to the October 31 departure date could still be required even if a deal were agreed in the coming days, as time would still be needed to fine-tune the agreement.

European Commission head Jean-Claude Juncker said it was up to Britain to decide whether to ask for an extension.

"But if Boris Johnson were to ask for extra time - which probably he won't - I would consider it unhistoric to refuse such a request," Juncker told Austrian media outlet Kurier.

The Sunday Times reported that Johnson would speak to German Chancellor Angela Merkel, French President Emmanuel Macron and Juncker by the end of Monday.

Australian Associated Press