Theresa May has written to Jeremy Corbyn offering further talks with Labour in an attempt to secure cross-party support for her Brexit deal.

The prime minister questioned Mr Corbyn's key call for the UK to remain in a customs union with Brussels, but offered concessions in other areas, and said she wanted talks between Labour and Tory teams "as soon as possible".

Her offer came as Brexit Secretary Stephen Barclay prepared for talks with European Union chief negotiator Michel Barnier, as the government stepped up efforts to secure changes to the Irish backstop measure in the Withdrawal Agreement.

In her letter to Mr Corbyn, responding to the conditions for a Brexit deal set out by the Labour leader, the prime minister said she wanted the Tory and Labour teams to consider "alternative arrangements" to the Irish backstop.

In response to his demand for a customs union, Mrs May insisted her deal met many of the conditions he had set.

She said the existing Political Declaration – the part of the Brexit deal setting out the goals for the future UK-EU relationship – "explicitly provides for the benefits of a customs union – no tariffs, fees, charges or quantitative restrictions across all sectors and no checks on rules of origin".

But she said it also recognises the development of the UK’s independent trade policy.

Brexit secretary Stephen Barclay will meet Michel Barnier on Monday. Credit: PA

Mr Corbyn’s demand is for a customs union that gives the UK a say on future trade deals the EU might strike – something Brussels appears unlikely to accept.

The prime minister said: "I am not clear why you believe it would be preferable to seek a say in future EU trade deals rather than the ability to strike our own deals?"

She also questioned whether the call for completely "frictionless" trade would mean reneging on Labour's commitment to end free movement by requiring single market membership.

The prime minister has previously ruled out a customs union, which would restrict the UK's ability to strike trade deals, and could face Cabinet resignations if she changed her position.

Treasury chief secretary Liz Truss refused to rule out resigning if Mrs May backed a customs union.

Mrs May called for urgent talks with Jeremy Corbyn. Credit: PA

Mr Corbyn called for UK standards to keep pace with evolving standards across Europe.

Mrs May rejected automatically following EU rules on workers' rights and environmental protection but "in the interest of building support across the House" she said the Government is prepared to commit to asking Parliament if it wishes to follow suit if standards change.

In her response to the Labour leader’s letter setting out his conditions to support a Brexit deal, Mrs May said: "It is good to see that we agree that the UK should leave the European Union with a deal and that the urgent task at hand is to find a deal that honours our commitments to the people of Northern Ireland, can command support in Parliament and can be negotiated with the EU – not to seek an election or second referendum."

Mr Corbyn has repeatedly said there should be an election if Mrs May cannot get a deal through Parliament and he has faced concerted pressure from some in his party to push for a second public vote.

There appears little prospect of an imminent breakthrough with Brussels, and Mrs May might not bring her deal back for a decisive vote this month.

Labour will use a vote expected on Thursday to attempt to force the Prime Minister to bring the deal back for a showdown by February 26 to prevent her "running down the clock" before Brexit.

But the prime minister is expected to offer MPs a further chance to vote on non-binding amendments which could influence her Brexit strategy on February 27.

The move is aimed at postponing a rebellion by ministers who are committed to removing the possibility of the UK crashing out of the EU without a deal on March 29.

Pro-EU Tories Heidi Allen and Sarah Wollaston both said ministers should “step up” this week to prevent a no-deal Brexit.

And shadow Brexit secretary Sir Keir Starmer said Mrs May could not keep delaying.

"We will wait and see what the Government comes back with on Thursday, but we have got to put a hard stop to this running down of the clock," he said.

"The prime minister is pretending there is progress in the talks. However, the reality is that she is using up the remaining time to try and impose a binary choice between her deal and no deal.

"This week Parliament needs to say enough is enough -and take control of what happens next."