The European Union is ready to give the UK the unilateral right to leave the customs union, chief negotiator Michel Barnier has said in a bid to make the Brexit deal acceptable to the UK parliament.

He stressed, however, that Britain would still need to honour its commitment to preserve a border free of controls between the Republic of Ireland and Northern Ireland.

That is something that in previous negotiations led to proposals to place a customs border "in the Irish Sea".

Just three weeks before Britain is due to leave the EU on 29 March, the divided UK parliament has yet to approve the EU-UK Brexit deal.

British Prime Minister Theresa May today called on the EU to make "one last push" to break the deadlock.

However, she also warned MPs that the UK may never leave the European Union if MPs reject her plan.

At the heart of the House of Commons' opposition to the already-negotiated divorce deal is the backstop, a provision to keep the Irish border open after Brexit.

The eurosceptic wing of Mrs May's Conservative party fears it could trap the UK in the EU's trading rules forever.

"EU commits to give UK the option to exit the Single Customs Territory unilaterally, while the other elements of the backstop must be maintained to avoid a hard border," Mr Barnier tweeted after briefing ambassadors of the 27 EU states that are staying on together after Brexit.

"UK will not be forced into customs union against its will," he added.

Responding to Mr Barnier's tweets this afternoon, a spokesman for the Government said: "These negotiations on the political declaration are taking place between Michel Barnier's Taskforce and the UK.

"The Government welcomes the fact that Michel Barnier continues to stand up for the interests of the whole of the EU, including Ireland.

"The Taoiseach has repeatedly made clear that he would not oppose a backstop which is specific to Northern Ireland, if that is deemed helpful, but that would have to be a decision for the UK."

4/5 EU commits to give UK the option to exit the Single Customs Territory unilaterally, while the other elements of the backstop must be maintained to avoid a hard border. UK will not be forced into customs union against its will. — Michel Barnier (@MichelBarnier) March 8, 2019

Read more:

Michel Barnier's Brexit tweets explained

EU's compromise may still be unpalatable to London

As Brexit goes down to the wire, fears on both sides of the Channel are growing about the economic damage in the event that Britain leaves the EU abruptly without any transition agreement to soften the resulting disruption to trade.

While Mr Barnier's latest proposal would make legally binding commitments of the assurances the EU offered to London in January, it is unlikely to be seen as enough by many of the harder eurosceptics.

"The EU will continue working intensively over the coming days to ensure that the UK leaves the EU with an agreement," Mr Barnier said, as British and EU negotiators held more talks today.

They were due to continue through the weekend.

Mr Barnier said the EU was ready to legally commit to using its "best endeavours" in trade negotiations with Britain after Brexit to find a solution that made sure the border remained open, and the contentious backstop was never applied.

Mr Barnier will travel to Dublin this weekend for what has been described as a "private" and "low key" visit.

It is understood he will attend the Ireland-France rugby match on Sunday with his two sons.

It is not clear if there are any meetings scheduled with Government figures.

Quick thread on the Barnier statements:

This essentially going back to the NI-specific backstop: ie, if it really wants to, the UK can leave the Single Customs Territory, but NI would remain. "The other elements of the backstop must be maintained to avoid a hard border" — Tony Connelly (@tconnellyRTE) March 8, 2019

DUP deputy leader Nigel Dodds said Mr Barnier's proposal was neither "realistic nor sensible".

"It disrespects the constitutional and economic integrity of the United Kingdom," he said.

"This is an attempt to get ahead of a possible blame game and appear positive when in reality it is going backwards to something rejected a year ago.

"As the Prime Minister has said, 'no United Kingdom Prime Minister' could sign up to an arrangement which annexes Northern Ireland from the rest of the United Kingdom.

"Whilst the European Union has spoken often about their value of the peace process in Northern Ireland, this proposal demonstrates that they have a one-sided approach and a lack of understanding about the divisions in Northern Ireland."

Brexit Secretary Steve Barclay also dismissed Mr Barnier's proposal.

He tweeted: "With a very real deadline looming, now is not the time to rerun old arguments. The UK has put forward clear new proposals. We now need to agree a balanced solution that can work for both sides."