Theresa May in Brussels talks with Jean-Claude Juncker and Michel Barnier in bid to ease Brexit talks

Downing Street sources insisted the meeting had "been in the diary for weeks" but the announcement caused surprise in Westminster and was not in Mr Juncker’s pre-released diary.

It comes after last week's negotiations ended with little movement.

Mrs May, who will be joined by Brexit Secretary David Davis, is expected to have discussions with European counterparts over the coming days ahead of a meeting of all EU leaders later in the week.

No 10 said the PM and Angela Merkel, the German Chancellor, had agreed the "importance of continued constructive progress" in the UK's exit negotiations in an early morning telephone call on Sunday.

Over dinner, the PM will hope to end the stalemate over the divorce settlement that is stopping post-Brexit trading relationship being discussed.

After the fifth round of discussions were brought to a close last week, Mr Barnier said he would not recommend that talks moved on to the next stage when he attends the European Council on Thursday.

The EU’s chief negotiator bemoaned how the negotiations had ended without making any "great steps forward" and there was "disturbing deadlock" over the size of Britain's divorce bill.

Mr Juncker said the Brexit process will take "longer than we initially thought," blaming delays on Britain's failure to settle its financial obligations.

The Government wants EU leaders to expand Mr Barnier's negotiating mandate to allow some headway to be made.

David Jones, the former Brexit minister, however, said Britain should suspend negotiations until the EU was prepared to talk "sensibly about money" as well as future trade terms.

Yet Labour's John McDonnell suggested Tory MPs were in talks with Labour to prevent Britain leaving the bloc without a deal.

The Shadow Chancellor said the UK Parliament could stop the Tory Government taking the country out of the block without an agreement in place and claimed discussions were "going right the way across the House".

But Chris Grayling, the Transport Secretary, said the Labour MP was talking "nonsense" and accused him of threatening to create a chaotic Brexit.

He insisted Britain would "succeed whatever happens" but claimed farmers would "grow more here" if the UK left without a deal.

This morning, Ken Clarke, the former Conservative Chancellor, said Mrs May needed to convince European leaders that the Government could deliver an agreement as he insisted that Parliament could constitutionally block a no-deal exit from the EU if it chose to.

Asked if Parliament had the power to veto a no-deal option with the consequence that Britain would remain in the EU, Mr Clarke told BBC Radio 4's Today programme: "As an off-the-cuff constitutional legal reply, yes, it does. This is a parliamentary democracy, Parliament here can do, practically, what it likes.

"But a majority would wish to look in the round at whatever this crisis scenario is that has arisen at the time."

Mr Clarke said his proposed amendments to the EU Withdrawal Bill were not intended to reverse leaving, but to bind "ultra-right" members of the Cabinet to ensure the UK got the best Brexit deal.

"Parliament, if we amend this Bill properly, can start binding in the ultra-right members of the Cabinet, and the ultra-left members of the shadow cabinet, into going in that direction."

The europhile backbencher said a no-deal situation would be “catastrophic” for the UK economy in the short term.

In what is likely to be seen as a dig at Boris Johnson, the Foreign Secretary, Mr Clarke said: "We mustn't be seduced by this bizarre stuff of the lion roaring and of President Trump and the Japanese and protectionist countries around the world all being prepared to open their markets to us; no rules we have got to comply with and no obligations. Just 'come and sell us whatever you want'.

"This is compete fantasy. It's la-la land. It's going down the rabbit hole with a white rabbit," added the Nottingham MP.