LONDON and Brussels are to “intensify” the Brexit talks with officials meeting every day until the crunch EU summit on October 17.

The commitment came over a working lunch of snails, salmon and cheese between Boris Johnson and Jean-Claude Juncker, the outgoing President of the European Commission.

A No 10 spokeswoman said: “The Prime Minister and President Juncker had a constructive meeting this lunchtime. The Brexit Secretary and Michel Barnier were also in attendance.

“The leaders took stock of the ongoing talks between the UK’s team and Taskforce 50. The Prime Minister reconfirmed his commitment to the Good Friday/Belfast Agreement and his determination to reach a deal with the backstop removed, that UK parliamentarians could support.

“The Prime Minister also reiterated that he would not request an extension and would take the UK out of the EU on the 31st October.”

She added: “The leaders agreed that the discussions needed to intensify and that meetings would soon take place on a daily basis.

“It was agreed that talks should also take place at a political level between Michel Barnier and the Brexit Secretary and conversations would also continue between President Juncker and the Prime Minister”.

Earlier, Mr Johnson said he was “cautious” about progress being made in the Brexit talks after he met Mr Juncker in their first face-to-face meeting.

They shook hands in a cordial welcome at Le Bouquet Garni in Luxembourg City’s medieval heart.

The setting of a closed-off restaurant situated in an 18th century house, and not an EU or UK building, was said by officials to be a “neutral location” for their Brexit discussions.

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Boris Johnson and Jean-Claude JunckerBoris Johnson said he was ‘cautious’ of Brexit progress after meeting Mr Juncker (Stefan Rousseau/PA)

They explored the possibilities of striking a fresh deal but, despite the warm greetings, their rhetoric has so far suggested they remain far apart, with the Irish backstop to prevent a hard border remaining a major sticking point.

Michelin guide inspectors described the restaurant as being “steeped in charm” and seeking to “enhance and develop the strength of classical dishes”.

The “menu gourmand” costs 55 euro – or £48 with the falling price of sterling amid Brexit chaos and uncertainty.

Foie gras, fillet of beef with an apple fondant and mushrooms or “the inevitable” creme brulee are all options for the customer with a big enough wallet.

While the restaurant itself was closed to the public, the streets were not and British Remain-backers headed to the square to make their voices known to the PM and to call for a second vote.

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Brexit Secretary Stephen Barclay and No 10 negotiator David Frost were also expected to travel to Luxembourg, where Mr Juncker was prime minister for 18 years.

Writing in the Daily Telegraph ahead of the meeting, Mr Johnson said he was working “flat out” for an agreement but that he would force through Brexit even if a deal cannot be reached at the European Council summit next month.

“But be in no doubt that if we cannot get a deal – the right deal for both sides – then the UK will come out anyway,” he added.

A Downing Street source said any further delay would be a “huge mistake” which would pile on “additional long months of rancour and division”.

“This is why the PM will stress to Mr Juncker that, while he wants to secure a deal, if no deal can be agreed by October 18 his policy is to leave without a deal on October 31 – and reject any delay offered by the EU,” the source said.

(PA Graphics)(PA Graphics)

The Benn Act passed by Parliament after MPs seized control of Commons business requires the PM to seek an extension to the Brexit process if a deal has not been reached by October 19.

Foreign Secretary Dominic Raab suggested the Government was still examining the implications of the legislation.

“The UK Government is always going to behave lawfully,” he told BBC Radio 4’s Today.

“At the same time, the legislation that was required, the surrender bill, is deeply, deeply flawed.”

Downing St has sought to downplay speculation that Monday’s meeting would be a breakthrough moment and Mr Barclay said on Sunday that while there was still “significant work” to do to reach an agreement, a “landing zone” for a deal was in sight.

With Mr Johnson needing to break the deadlock in Parliament, he must find an alternative to the Irish backstop, which aims to prevent a hard border returning to the island of Ireland.

There have been suggestions that the PM is planning an alternative that would keep Northern Ireland more closely aligned with the EU than the rest of the UK.

Mr Juncker, in an interview on German radio, said “time is running out” for an alternative, as he suggested no-deal was unpatriotic.

“If you love your country – and I assume there are still patriots in the UK – you do not want to wish your country such a fate,” he said.

Mr Johnson was due to meet the Luxembourg’s current prime minister, Xavier Bettel, for further talks in the afternoon.