Theresa May heads to Brussels for Brexit talks as Gibraltar row rumbles on

But Spanish Prime Minister Pedro Sanchez has threatened to “veto” progress without further guarantees for Madrid over the status of Gibraltar.

Pedro Sanchez has threatened to ‘veto’ progress on Brexit (Desmond Boylan/AP)

Mrs May also faced domestic difficulties, with her relationship with the Democratic Unionist Party looking increasingly strained as Arlene Foster’s party prepared for its conference in Belfast.

DUP leader Arlene Foster warned that the confidence and supply deal propping up Mrs May’s minority administration would have to be “revisited” if her Brexit deal gets through Parliament.

The DUP has strongly opposed the deal and the guest star at its conference will be Boris Johnson, a prominent critic of the Prime Minister’s approach and a potential rival for the Tory leadership.

DUP leader Arlene Foster and deputy leader Nigel Dodds have strongly opposed Theresa May’s deal (Brian Lawless/PA)

The tensions over Gibraltar concern Spain’s demand that Gibraltar’s future is considered a bilateral issue between London and Madrid rather than between the EU and UK.

Mr Sanchez has suggested that Sunday’s summit could be scrapped unless there is a breakthrough.

Mrs May has insisted her deal is in the interests of “the whole UK family” including Gibraltar.

The last-minute diplomatic spat comes as Mrs May’s critics laid bare the scale of their opposition to the Brexit plan.

More than 80 Conservative MPs – from both the Leave and Remain sides – are threatening to vote against the agreement.

And if it did pass the Commons, the repercussions could bring down Mrs May’s Government, with the DUP hinting at withdrawing the support of its MPs.

The DUP’s 10 MPs have proved reluctant to vote with the Government since the terms of the Brexit deal became known and the termination of their Westminster arrangement would be a major blow to the Prime Minister.

In her conference speech, Mrs Foster will say: “The choice is not between this deal and no deal despite what the Government spin machine may say.

“The reality is that if we are to secure a better outcome than is currently on offer then the only option is to look beyond this current draft Withdrawal Agreement and work in the time ahead for an improved outcome.”

The DUP’s Westminster leader Nigel Dodds will use his conference speech to stress that the confidence and supply arrangement is with the Conservative Party – rather than Mrs May herself – and urge Tory Eurosceptics to revolt against the Brexit deal.

“The confidence and supply deal is a two-way street. The Government’s commitments under it are clear… including on Brexit.

“Commitments freely entered into must be delivered and if they are not, then clearly, as we have shown, there are consequences.”

In a message aimed at Tory Brexiteers he will say: “Our agreement is of course with the Conservative Party.  It is incumbent therefore on all Conservatives in Parliament who recognise the importance of continuing stability and who wish to see the Government deliver its agenda to ensure it is honoured in full.”

But Mrs May, who launched an effort to sell the Brexit deal directly to the public, insisted that there would be no changes to appease critics at this late stage.

In a BBC phone-in she said: “If we were to go back to the European Union and say ‘People didn’t like that deal can we have another one?,’ I don’t think they are going to come to us and say ‘We will give you a better deal’.

“This is the deal that I think works for the UK.”

The Daily Telegraph reported that the next stage of her Brexit sales pitch will be on the immigration controls believed to have been a key factor in the Leave vote.

According to leaked Cabinet papers, the Home Office has drawn up plans to issue low-skilled migrants with 11-month visas “with restricted entitlements and rights” while they are living in the UK.

Alternative plans could allow EU migrants aged between 18 and 30 to live and work in the UK for two years, with a strict cap on numbers.

The Government will abolish the cap on highly skilled “tier 2” migrants entirely, the report said, with the plans set out in the week beginning December 3 – a week before the crunch Brexit vote is expected in the Commons.

Dominic Raab has claimed the UK will be worse off under Mrs May’s deal than if it stayed in the EU (Andrew Matthews/PA)

Despite the turmoil, the Prime Minister again insisted that as far as she was concerned, Brexit would go ahead next year as planned.

“Personally, there is no question of no Brexit, because the Government needs to deliver on what people voted for in the referendum in 2016,” she said.

“As far as I am concerned, the UK is leaving the European Union on March 29 2019.”