Boris Johnson faces a race against the clock to secure a Brexit deal and get Tory Eurosceptics and the DUP onside to back him.

The Prime Minister carried out a charm offensive in Downing Street on Tuesday evening as he held a series of talks with backbenchers and the leaders of the DUP.

Meanwhile, his negotiating team worked through the night as reports increased that a deal was nearing, with a solution said to be forthcoming on the Irish border.

Mr Johnson knows he must have members of the European Research Group (ERG), a band of hardline Tory Eurosceptics, on board or his deal has little chance of making it through a vote in the House of Commons.

It was his predecessor Theresa May’s failure to secure the ERG’s support that led to her Withdrawal Agreement being defeated three times.

But, despite a flurry of meetings at Number 10, there were reports that Mr Johnson’s exit terms were causing splits in the ERG.

Chair Steve Baker MP, speaking outside Downing Street, said he was “optimistic” that Mr Johnson’s team in Brussels would finalise a “tolerable deal that I will be able to vote for”.

Mark Francois said the meeting was “interesting” and added “there’ll be further chats to have”, while former Tory leader Iain Duncan Smith and anti-EU battler Sir Bill Cash MP also emerged from Downing Street.

Jacob Rees-Mogg, the leader of the Commons and a former ERG chair, told LBC: “I think the votes are there now for a deal.”

We await the full details of the new deal to see exactly how they address the objections to the dead Theresa May deal, but dual-tariff systems like this would be, as Priti Patel has said, unacceptable

Owen Patterson MP, former environment secretary

But, in an interview with The Sun, former environment secretary Owen Paterson dubbed it “unacceptable” that Mr Johnson was reportedly preparing to agree to a border down the Irish Sea, creating custom checks on goods travelling between Northern Ireland and Great Britain.

The Guardian reported senior sources on both sides of the Channel saying that a draft treaty could be published on Wednesday morning after the UK agreed in principle there will be a customs border in the Irish Sea.

While still in office, Mrs May said such an arrangement could never be accepted by a British prime minister.

Mr Paterson said: “We await the full details of the new deal to see exactly how they address the objections to the dead Theresa May deal, but dual-tariff systems like this would be, as Priti Patel has said, unacceptable.”

The DUP, in a statement after their second audience with the PM in as many days, were also decidedly lukewarm on the mooted proposals.

“We respect the fact negotiations are ongoing and therefore cannot give a detailed commentary but it would be fair to indicate gaps remain and further work is required,” a spokesman said.

Leader Arlene Foster and her deputy Nigel Dodds slipped out of the back exit of Downing Street and avoided waiting journalists following the meeting.

Number 10 officials were privately playing down suggestions of a Brussels breakthrough and the PM’s decision to hold Cabinet in the late afternoon indicated that negotiators still require time to finalise a deal before Thursday’s crunch European Council summit.

Addressing journalists on Tuesday, the PM’s official spokesman said: “Talks remain constructive but there is more work still to do.”

A deal will need to be published, along with a legal text, if the EU27 are to consider ratifying the Withdrawal Agreement at their gathering this week, meaning the pressure is on to sign off on the draft agreement.

Michel Barnier, the EU’s chief negotiator, warned Mr Johnson it was “high time to turn good intentions into legal text”.

Irish Taoiseach Leo Varadkar, in a press conference in Dublin, said it remained uncertain whether a deal would be ready in time for the Brussels summit.

“The initial indications (from the EU) are that we are making progress, negotiations are moving in the right direction,” he told reporters.

“But whether we will be able to conclude a revised Withdrawal Agreement, which is an international treaty, in time for the summit, that’s as of now unclear.”

Mr Varadkar also revealed that the PM told him during their meeting last week he was “confident” he would be able to do what Theresa May thrice failed to do by getting a deal through the House of Commons.

Taoiseach Leo Varadkar said he was unsure if a deal would be ready for the European Council summit Credit: Niall Carson/PA

Downing Street officials are understood to have been meeting with various parliamentary factions in recent days as negotiators hammer out a deal.

Mr Barnier struck a positive note after meeting Brexit Secretary Stephen Barclay at the General Affairs Council on Tuesday morning.

He debriefed EU27 ministers in Luxembourg before tweeting: “Talks are difficult but I believe an agreement is still possible.”

Meanwhile, Downing Street said Mr Johnson told French president Emmanuel Macron in a phone call that UK officials would “continue to work hard” on securing a Brexit deal.

The two-day EU summit is crucial because the PM must get a new deal approved by MPs by Saturday if he is to avoid a clash over asking for a Brexit delay.

The Benn Act passed by MPs opposed to a no-deal, including Tory rebels, says he must ask for an extension to Article 50 if MPs do not back a deal by then.

There are fears that a loophole could be used to avoid this, with the PM repeatedly ruling out making the extension request under his “do or die” pledge to get Brexit done by the Halloween deadline.

Regardless of the outcome in Brussels, a showdown is anticipated in an emergency sitting of Parliament on Saturday, the first in 37 years, if the Government requests the unusual move and it is backed by MPs.

Mr Johnson, if he intends to ask MPs to sit on Saturday, must put a motion before the Commons on Wednesday, which will be voted upon on Thursday.

During the weekend session, they will be able to back or reject any deal presented to them, or there will be discussions on what to do next in the Brexit saga.

The Liberal Democrats have put forward an amendment to the Queen’s Speech for Tuesday to test whether there is support for a second referendum.