Boris Johnson will travel to Brussels tomorrow in a last-ditch bid to secure a post-Brexit trade talks breakthrough.
The prime minister is due to sit down with European Commission President Ursula von der Leyen for dinner to continue discussions, after the pair's phone call on Monday which ended with "significant differences" still in place.
Their showdown will come a day before EU leaders land in the Belgian capital for a pre-Christmas summit.
Ms von der Leyen said "I look forward to welcoming" Mr Johnson to Brussels on what will be his first trip there since winning an election landslide last year and delivering Brexit.
Earlier during a visit to an NHS site on Tuesday as the Pfizer COVID-19 vaccine is rolled out across the UK, the prime minister issued a warning that a trade agreement might not be struck.
"You've got to be optimistic, you've got to believe there's the power of sweet reason to get this thing over the line," he said.
"But I've got to tell you it's looking very, very difficult at the moment.
"We'll do our level best, but I've would just say to everybody - be in good cheer, there are great options ahead for our country on any view.
"But the key thing is, on 1 January, whatever happens there's going to be change and people need to get ready for that change."
The prime minister said there "may come a moment when we have to acknowledge that it's time to draw stumps" and settle on a no-deal outcome ahead of the end of the Brexit transition period on 31 December.
He added the UK and the EU are "a long way apart still" on the issue of fisheries.
The prime minister and Ms von der Leyen have also highlighted so-called "level playing field" commitments and governance issues as other major sticking points.
Mr Johnson urged European leaders to "understand that the UK has left the EU in order to be able exercise democratic control over the way we do things".
And he vowed Britain would "prosper mightily" whatever the outcome of trade negotiations.
Without a post-Brexit trade deal being agreed by the end of this month, the EU and UK are likely to have to trade on World Trade Organisation rules with tariffs imposed in both directions.
The prime minister has often referred to this scenario as "Australian" terms of trade with the bloc, as Australia does not have a comprehensive trade deal in place with the EU.
The EU's chief negotiator, Michel Barnier, met with his UK counterpart, Lord Frost, on Tuesday to "prepare the next steps" ahead of the meeting between Ms von der Leyen and the prime minister.
Speaking as he prepared to brief EU ministers on the current state of Brexit negotiations, Mr Barnier said the trade talks needed "a school of patience, even a university of patience".
After the meeting, Mr Barnier said there was "full unity" among the 27 EU member states, adding: "We will never sacrifice our future for the present. Access to our market comes with conditions."
An EU source said Mr Barnier had told member states that the "chances of reaching an agreement are now very slim".
Lord Frost was due to travel back to London later on Tuesday in order to brief Mr Johnson on the remaining differences between the UK and EU negotiating teams.
Downing Street said there were "no plans" for the prime minister to meet with French President Emmanuel Macron or German Chancellor Angela Merkel.
Mr Johnson's official spokesman said a date of the meeting between the prime minister and Ms von der Leyen had yet to be agreed.
Number 10 also did not rule out MPs being made to sit over the Christmas period in order to approve a Brexit deal, but said that negotiations would not continue into 2021.
Speaking in Brussels on Tuesday, Germany's Europe minister Michael Roth called for "political will in London" in order to reach an EU-UK trade deal.
"It's good that every effort is undertaken to find a sustainable and good solution," he said.
"We want to reach a deal but not at any price. What we need is political will in London. Let me be very clear, our future relationship is based on trust and confidence.
"It's precisely this confidence that is at stake in our negotiations right now."
EU leaders are due to gather in Brussels on Thursday for a European Council summit, although Brexit is not yet on the agenda.
