GERMAN chancellor Angela Merkel has given an upbeat assessment of Brexit talks, saying that she sees no reason why they should not succeed.

Mrs Merkel was speaking after Theresa May issued a direct plea to EU leaders to clear the way for a deal which she can sell to British voters.

Amid growing pressure from hardline Eurosceptics in her own party to prepare for a no-deal Brexit, the Prime Minister told leaders of the remaining 27 states that they face a "clear and urgent imperative" to give new impetus to stalled negotiations if they are to get an outcome which is acceptable to both the British public and their own people.

The EU27 will declare at the European Council in Brussels on Friday that insufficient progress has been made in withdrawal negotiations for trade talks to begin as Britain wants, with several leaders making clear they want more "clarity" about how much the UK is willing to pay in its Brexit "divorce bill".

But they are expected to offer Mrs May a glimmer of hope by agreeing to start internal "scoping" work on their trade stance ahead of a possible green-light for the second phase of negotiations, dealing with trade and the transition to Brexit, at their next gathering on December 14-15.

Addressing her fellow leaders over dinner in Brussels, Mrs May left no doubt that she needs their help to deliver a deal that is acceptable to British voters.

"There is increasingly a sense that we must work together to get to an outcome we can stand behind and defend to our people," she said.

Calling for "joint effort and endeavour" to inject momentum into the talks process, she told them: "The clear and urgent imperative must be that the dynamic you create enables us to move forward together."

In an early-hours press conference following the dinner, Mrs Merkel brushed aside suggestions that the Brexit talks might collapse, saying they were making progress "step by step".

"I have no doubt that if we are all in clear minds... We are going to achieve a good outcome," said the German Chancellor. "As far as I am concerned, I don't hear any reason to believe that we are not going to be successful."

Mrs Merkel said she was "highly motivated" to work on a new mandate for chief Brexit negotiator Michel Barnier which might permit trade talks to begin in December, but warned that the second stage of talks would be "more complicated than the first".

On the divorce issues dealt with in the first stage, there was "by and large general agreement" on the future status of the Irish border and "headway" was being made on expats' rights after Brexit, but Mrs May made no specific new offer on Britain's financial settlement, she said.

Dutch Prime Minister Mark Rutte said the EU27 need "more meat on the bone" of Britain's exit payment, following Mrs May's promise in a speech in Florence last month that the UK would honour financial commitments made as an EU member.

The offer made by Mrs May in Florence is believed to amount to around 20 billion euro (£18 billion), while Brussels is understood to be seeking something closer to 60 billion euro (£53 billion).

Mrs Merkel and French president Emmanuel Macron made a very public show of support for the Prime Minister on the first day of the council, engaging her in prolonged conversation - characterised by a senior British source as "very constructive and friendly" - on their way into the summit chamber.

The scenes made a strong contrast with last December, when the PM appeared isolated with no-one to talk to as the leaders gathered round the table.

A senior UK Government source acknowledged that the summit took place against a "difficult political backdrop" for the PM.

Failure to secure the go-ahead for trade talks this month has fuelled pressure on Mrs May to begin expensive preparations for a "no-deal" Brexit.

And a group of hardline Brexiteers including four Tory former cabinet ministers led by ex-chancellor Lord Lawson signed a joint letter urging her to walk away from talks.

Writing in the Daily Mail, former Conservative leader Iain Duncan Smith said Brussels was "dragging its feet".

He added: "All talk about 'sufficient progress' in talks is of course a crude smokescreen to disguise a naked attempt to force the UK into a divorce bill - as much as £90 billion - with nothing in return. That is why the talks have stalled."

Sources close to David Davis dismissed a report that the Brexit Secretary is preparing to present an "upbeat" assessment of a no-deal exit from the EU to the Cabinet at a meeting on October 31.

Mrs May made no comment to waiting reporters as she arrived for a leaders' breakfast at the European Council venue.

The Prime Minister was also expected to hold talks with Council president Donald Tusk before leaving the summit early as the remaining 27 leaders discuss their assessment of progress on Brexit in her absence.

Maltese Prime Minister Joseph Muscat said Mrs May had delivered "her best performance yet" at Thursday evening's dinner, but that her intervention had not "really changed anything".

"It conveyed a warm, candid and sincere appeal that she wants progress to be made, that she has moved in her position," said Mr Muscat. "I think it was appreciated."

Mr Muscat added that "problems" remain in the Brexit process and that he did not expect the EU27 to clear the way for trade talks at this summit.

But he said: "I think the wording in today's conclusions will show that there is willingness on the EU side to move forward."

Austrian Chancellor Christian Kern said: "It's OK to see that there is at least some rhetorical progress, but unfortunately we need to come to conclusions, because uncertainty is not good for the continent, is not good for our economy.

"It is up to the British Government to propose something which is really a basis and a ground for further progress, which is totally important."

Lithuanian President Dalia Grybauskaite said Mrs May needed to move "from words to real deeds".

"I hope that she will be able to have a success in December," said Ms Grybauskaite. "It is time for real negotiations and not just negotiating in the media with rhetoric."

Asked if Mrs May's address over dinner had been her best intervention in the process yet, she replied: "If you talk about rhetorical abilities, maybe. But for negotiations, you need concrete negotiation abilities, not only rhetoric."

European Commission president Jean-Claude Juncker said he was not expecting a "miracle" at Friday's talks of the kind that would clear the way for an immediate start of trade talks.

The EU27 leaders will consider the progress made in Brexit talks so far, said Mr Juncker, adding: "I don't think that there will be a miracle."

Responding to Mrs May's speech, he said: "We have some details but we don't have all the details we need. But work is going on."

Irish Taoiseach Leo Varadkar said Mrs May told Europe's leaders that she will not accept a physical border on the island of Ireland.

He said her address at the summit was very good and positive, and her language on the issue has strengthened.

"She specifically referenced the unique situation for both Ireland and Northern Ireland, which I think was very positive," he said.

"She strengthened her language in relation to the border.

"She said the UK would not accept a physical border on the island of Ireland - again very positive language."

The Taoiseach repeated his call for more detail on the border question.

Responding to reports that Mr Davis was planning to present a "no-deal" plan to Cabinet, a spokesman for the Department for Exiting the EU said: "It is in everyone's interests to secure a good deal for both sides.

"We think that is by far and away the most likely outcome, but we have a duty to plan for the alternative."