Theresa May is in Brussels for a dinner later with EU leaders in a bid to end a stalemate over Brexit.
The meeting, with chief negotiator Michel Barnier and Commission chief Jean-Claude Juncker, comes days after the pair said talks were in "deadlock".
Brexit Secretary David Davis is joining Mrs May for the meeting, ahead of this week's summit of EU leaders.
Mr Juncker said details of the dinner would be revealed in an "autopsy" afterwards.
Although Mrs May's trip to Brussels was not made public during last week's negotiations, Downing Street sources insisted it had "been in the diary for weeks".
Over a dinner expected to last 90 minutes, the PM hopes to end a stalemate over the three initial topics for negotiation - the amount the UK owes the EU when it leaves, the future rights of EU citizens in the UK and UK citizens living in the EU, and what happens on the Northern Ireland border.
The EU side says that until "sufficient progress" is made on these three items they will not begin discussing the UK's post-Brexit relations - things like trade arrangements and defence.
BBC assistant political editor Norman Smith said the negotiations were entering a "critical phase", with the possibility of the UK leaving without a deal in place becoming the "new front line" in the debate about Brexit.
The UK is doing contingency planning for such an outcome, which both sides say they want to avoid.
Arriving at a meeting of EU foreign ministers in Luxembourg, Foreign Secretary Boris Johnson said it was time to "get on" with the negotiations.
"It's ready for the great ship to go down the slipway and onto the open sea and for us to start some serious conversations about the future and the deep and special relationship we hope to construct," he added.
Conservative John Redwood predicted that "at the 11th hour" the EU would want to reach a free trade deal with the UK.
"But if we look as if we are weak, it's going to delay getting any sensible offer out of them," the former minister, who campaigned for Brexit, added.
Mr Redwood said the UK would "do just fine" if no deal was reached and that he was "fairly relaxed" about the prospect of the EU imposing tariffs on UK goods, because the UK could trade "perfectly successfully" on World Trade Organisation terms.
But pro-EU former Tory chancellor Ken Clarke said talks failing to reach an agreement would have a "catastrophic" effect on the UK economy.
Together with Labour's Chris Leslie, Mr Clarke is trying to amend the government's key Brexit bill to put the two-year transition period proposed by Mrs May into law.
He said this could "bind in" the "ultra-right" members of the cabinet and the "ultra left" members of the shadow cabinet and convince Brussels the PM had the UK Parliament's backing.
Mrs May hopes when the 27 EU leaders meet on Thursday and Friday, they will give Mr Barnier a mandate to start talks on future trade.
Ahead of the European Council meeting, the PM has discussed Brexit in phone calls with French President Emmanuel Macron and German chancellor Angela Merkel.
But Mr Barnier has said there is still no agreement on how much the UK should pay the EU when it leaves.
Last week an internal draft document suggested the EU was going to begin preparing for the possibility of trade talks beginning in December - provided the UK does more to bridge the gap on the key negotiating points.
Liberal Democrat leader Sir Vince Cable said there had been "failures on both sides" of the negotiating table so far, criticising the EU's "rigid" refusal to move the agenda forward.
But he said Mrs May had more to lose than EU leaders who "do not know whether to take her seriously" given Tory divisions over Brexit strategy.
He told BBC News: "Her own authority is very much at stake, and what she's got to do at this dinner is impress on the Europeans A) She's there to stay and B) What she is promising can be delivered - I think she's talking to a sceptical audience."