Michael Gove has suggested the government may ditch plans to ask MPs to vote on its EU Withdrawal Agreement Bill in the first week of June, following a backlash from all sides of the Commons.

Theresa May’s “new deal” unveiled yesterday has been savaged by Tory and Labour MPs and looks extremely unlikely to be able to survive a vote in the Commons.

Asked on BBC Radio 4′s Today programme on Thursday morning whether the Bill would definitely be voted on in the week beginning June 3, Gove said the government “will reflect over the course next few days”.

But speaking to MPs, May contradicted the environment secretary and said the Bill would be introduced.

May’s decision to offer MPs the chance to vote for a second referendum, in an attempt to woo Labour MPs, has infuriated her own backbenchers and led to calls that she bring forward her departure date.

She has promised to announce a timetable for her resignation once the WAB has its second reading.

But she faces a fresh bid to eject her from Downing Street sooner from the 1922 backbenchers’ committee which meets later today.

Keir Starmer, Labour’s shadow Brexit secretary, said this morning the prime minister should “pull the vote and pause”.

“What she announced yesterday isn’t going to work,” he told Today.

At least 30 Tory MPs who voted for the PM’s deal in the last vote have now said they can not support the Bill.

Leadership rivals Boris Johnson and Dominic Raab were among those who backed May’s deal in March but have vowed to oppose the WAB.

May hoped her 10-point compromise plan would woo enough Labour and DUP MPs to make up for Tory eurosceptics who are implacably opposed.

The last-ditch attempt to get a deal through included offering a vote on whether to hold a second referendum, as well as a choice over the UK’s future customs arrangements.

She said her deal was “one last chance” for MPs to deliver on the result of the 2016 referendum.