LONDON - MPs on all sides of the Brexit divide have vowed to vote down Theresa May’s withdrawal agreement when the government brings the bill to the House of Commons next month.

Downing Street said the key piece of Brexit legislation – the withdrawal agreement bill – would be voted on in the week beginning 3 June. “It is imperative we do so then if the UK is to leave the EU before the summer parliamentary recess,” a spokesman said.

Talks with Labour are to continue in the meantime. The prime minister met the Labour leader, Jeremy Corbyn, on Tuesday night, though no substantive progress has been made towards a cross-party agreement.

The Democratic Unionist party’s Westminster leader, Nigel Dodds, said it was “highly likely” May’s deal would be defeated again unless the prime minister can “demonstrate something new that addresses the problem of the backstop”. He added: “The prime minister has not pursued the one option that has ever achieved a positive vote for something in parliament. Alternative arrangements to the backstop won easily while everything else has failed.

“For the bill to have any prospect of success then there must be real change to protect the economic and constitutional integrity of the United Kingdom and deliver Brexit.”

The prime minister has not pursued the one option that has ever achieved a positive vote for something in parliament

The former environment secretary Owen Paterson, a member of the European Research Group, said nothing new had been put forward to convince hardline Brexiters in the Conservative party to vote for the agreement, and warned about the rise of Nigel Farage’s Brexit party.

“Sadly we will vote against it, yes, because as the DUP said in their statement, it doesn’t change the essential nature of the withdrawal agreement, which is unacceptable,” he told BBC Radio 4’s Today programme on Wednesday.

“People aren’t flocking to this new [Brexit] party’s rallies from the Tory party and the Labour party clamouring for the agreement, which has been the reaction of the government. They are going because they want to leave and they voted to leave, and they thought we were leaving on 29 March, and they feel thwarted and cheated.”