Theresa May has committed to giving MPs a say on a second Brexit referendum if they back her “new” make-or-break withdrawal deal next month.

The prime minister put the second referendum pledge at the heart of a ten-point “serious offer” designed to win MPs’ provisional backing for her Brexit deal.

She also offered parliament the right to vote on whether the UK should enter a temporary customs union with the EU after leaving – a compromise proposal already rejected by Labour – or stick to the government’s plan for customs.

And May will enshrine in law various promises already made to Tory Brexiteers and the DUP in an attempt to show the controversial Irish backstop will never be required.

May will be hoping, however, she has offered enough that MPs back her withdrawal agreement bill (WAB) at second reading – its first Commons stage – in June.

If it passes then, MPs will then get the chance to vote on a second referendum and customs arrangements, as well as amend the bill in others ways in future stages.

But her “one last chance” Brexit offer appeared to be dead on arrival as Remainers, Leavers, the DUP and former allies lined up to condemn her plan. 

Labour leader Jeremy Corbyn called it “largely a rehash” of what unfolded during the cross-party talks. 

“We will of course look seriously at the details of the Withdrawal Agreement Bill when it is published,” he said. “But we won’t back a repackaged version of the same old deal – and it’s clear that this weak and disintegrating government is unable deliver on its own commitments.”

If the measures fail to win over enough support, the PM faces having to leave office without having delivered Brexit, the main goal of her blighted premiership.

In a speech in Charing Cross, central London, May said a failure to reach agreement on Brexit would lead to a “nightmare future of permanently polarised politics”.

And explaining her offer designed to win cross-party support, she added: “I have tried everything I possibly can to find a way through.

“It’s true that initially I wanted to achieve this on the back of Conservative and DUP votes.

“In our parliamentary system that is simply how you normally get things done.

“I sought the changes MPs demanded, I offered to give up the job I love earlier than I would like.

“And on March 29, the day we were meant to leave the EU, if just 30 MPs had voted differently we would have passed the withdrawal agreement and we would be leaving the EU.

“But it was not enough.” 

As part of her offer to win over as many Tory Brexiteers as possible, May said the WAB would put the government under a legal obligation to develop “alternative arrangements” to the backstop, which creates a customs union with the EU to maintain an invisible Irish border, by December 2020.

For the DUP, she committed to the UK mainland being aligned with Northern Ireland on EU rules so the province is not treated differently and split off.

For Labour she also promised a workers rights bill to ensure the UK never undercuts EU rules, and pledged to stay in line with Brussels on environmental protections.

And she also backed calls from Labour MPs Lisa Nandy and Gareth Snell for parliament to be given a greater role in negotiations on a long term trade deal with the EU, once the UK has left.

The PM said: “This is a huge opportunity for the United Kingdom.

“Out of the EU. Out of ever-closer union. Free to do things differently.

“And doing so in a way that protects jobs, protects our security, maintains a close relationship with our friends and works for the whole United Kingdom.

“It is practical. It is responsible. It is deliverable.

“And right now, it is slipping away from us.

“We risk losing a great opportunity.”