Boris Johnson and European Commission president Ursula von der Leyen spoke via video conference on Saturday to take stock of progress in the negotiations following the final scheduled round of talks between Brussels and the UK this week.
The pair have tasked chief negotiators, Britain’s Lord Frost and the EU’s Michel Barnier, with intensifying the talks after acknowledging that “significant gaps remained” between the UK and Brussels.
The Prime Minister has set the deadline of the EU Council meeting on October 15 for securing a deal – only 12 days away.
A Downing Street spokesman said: “They agreed on the importance of finding an agreement, if at all possible, as a strong basis for a strategic EU-UK relationship in future.
“They endorsed the assessment of both chief negotiators that progress had been made in recent weeks but that significant gaps remained, notably but not only in the areas of fisheries, the level playing field, and governance.
“They instructed their chief negotiators to work intensively in order to try to bridge those gaps.
“They agreed to speak on a regular basis on this issue.”
Lord Frost, in a statement issued after his meeting with counterpart Mr Barnier on Friday, expressed concern there is “very little time now to resolve” the outstanding issues on fishing, state aid and governance before October 15.
But the agreement between Mr Johnson and Ms von der Leyen will pave the way for what is dubbed “the tunnel”, where the negotiating teams enter a media and briefing-free blackout in a bid to work out compromises on the outstanding differences.
The Prime Minister has struck a positive tone about the prospects of securing a trade deal in recent days, along with Cabinet Office minister Michael Gove, who is in charge of Britain’s Brexit preparations.
Mr Johnson told reporters on a construction site visit in west London on Saturday morning that there is a “good deal to be done” with the EU.
Vote Leave campaigner Mr Gove, speaking at the Conservative Party’s virtual conference, said: “I suspect there will be one or two ups and downs along the way but I am optimistic that we will get a deal.”
Foreign Secretary Dominic Raab, however, took a tougher approach in his conference speech, telling members the “days of being held over a barrel by Brussels are long gone”, as he stressed any trade deal must be “fair”.
Mrs von der Leyen on Friday said she believed a deal was still possible but warned time was running out without an intense period of negotiations.
She said the “most difficult issues” – including fisheries and state aid rules – still had to be resolved if they were to get an agreement in place by the end of the Brexit transition period on December 31.
“But where there is a will, there is a way, so I think we should intensify the negotiations because it is worth working hard on it,” she told a press briefing in the Belgian capital.