Parliament is heading for “an impasse” over Brexit that makes a further referendum on Theresa May’s proposed deal ever more likely, says Tony Blair.

The former Prime Minister dismissed the Government’s claim of a new unity and purpose – after the Chequers “away day” – arguing the Cabinet was still trying to “have cake and eat it”.

Mr Blair said there were still “irreconcilable differences” between ministers and, just as crucially, no majority in Parliament for any of the many proposed versions of Brexit.

“There is a real possibility of an impasse in Parliament,” he told BBC Radio 4’s World at One programme

In those circumstances, Mr Blair said, “the case is ever more stronger for this going back to people to allow them a final say in the deal that is actually agreed by the Government”.

Arguing “the Commons is key”, he added: “I think it is increasingly unlikely that they are going to get a proposition through the House of Commons.

“If they can’t, at that point, they are faced with a choice between an election and a referendum.”

The arch-Remain supporter also dismissed any chance of the EU agreeing to the Government’s proposal for “managed divergence” from Brussels regulations.

It would be rejected as an attempt to break free from the rules of the single market and customs union – which are required of everyone else – while the UK demanded to keep their benefits.

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“I will be really interested to see that deal,” Mr Blair said. “I literally don’t understand what they mean. This is cake and eat it.”

He also launched a fierce attack on senior Conservatives who are undermining the Good Friday Agreement that had brought peace to Northern Ireland – apparently viewing it as an obstacle to Brexit.

“It is not just alarming but sickening that people are seriously now saying that it doesn‘t matter if the Good Friday Agreement stays or it doesn’t stay,’ Mr Blair warned.

In an article for The Independent, attacking the “road to Brexit” series of speeches being made by senior ministers, Mr Blair wrote: “Each speech in this bizarre parade of Government ministers designed to show unity only further exposes the division.

“They all try to pull the sword out of the stone, huffing and puffing away, and all fail. This is because there is no escape from the binary nature of the choice over future trading arrangements.”

Mr Blair also issued a challenge to the Labour Party to oppose Brexit, as Jeremy Corbyn prepares to deliver his own key speech on withdrawal on Monday.

He released a study accompanying his article to show the economic pain from Brexit and that the UK needs EU migrants, adding: “It is good that the Labour Party position is “evolving”. But it must align it fully with its policy programme.

“To carry on pretending that there is Brexit and then, separate from Brexit, there is the NHS, education, crime etc. is ridiculous.

“If the evidence we present in this paper of all the economic forecasts is only half right, Brexit will reduce the scope for Government spending dramatically.”