Steve Brine, who quit to vote against government, says fresh referendum is now on table

Two ministers who resigned from the government on Monday night to back moves for parliament to take control of the Brexit process have said MPs are likely now to move towards a softer deal or a referendum.

Steve Brine, the former health minister who was among three to resign their posts to rebel against the government, said he believed that both revoking article 50 and a second referendum were now on the table.

Brine said he believed the prime minister’s deal was still “best of the options” but said that Conservative colleagues should realise “anything from here, as far as they are concerned, gets softer in terms of Brexit”.

MPs backed an amendment tabled by the former Tory minister Oliver Letwin on Monday night to give them control of the parliamentary timetable to allow backbenchers to hold a series of votes on alternatives to her Brexit deal. The prime minister has declined to say whether she will abide by the outcome of a process of “indicative votes”.

The former minister’s comments came as the health secretary, Matt Hancock, told Eurosceptics in his party that their only option now was to back Theresa May’s deal.

“It demonstrated that the option of no deal simply won’t be allowed by the Commons and that the best way through this impasse is the one deal that has been negotiated with the EU, that can be delivered quickly now,” he told BBC Radio 4’s Today programme. “The Commons is now absolutely clear it won’t allow [a no deal] and will legislate against if necessary.

“The options are narrowing and that demonstrates that if you want to deliver on the result of the referendum … then vote for the prime minister’s deal. Because the idea of voting against it in the hope of getting no deal is clearly now not going to happen.”

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Brine rejected suggestions that May could not pursue any outcome in parliament that contradicted the Conservative manifesto – which ruled out single market and customs union membership.

“You also have to remember that the manifesto of 2017 did not win a majority in the House of Commons,” he told the BBC. “And this is the crux of the whole matter, that the House of Commons and executive-led government works when you have got a majority in the House of Commons.”

Brine said all outcomes were on the table. “You have to accept that a second referendum or revoking article 50 are on the table because they will probably be some options,” Brine told BBC Radio 4’s Today programme.

Hancock said the government could not commit to implementing options that might be impossible. “We cannot say – absolutely, whatever they pass,” he said.

“If the Commons voted for the sun to rise in the west, the government would not be able to implement that. This whole debate has been characterised by people coming in with ideas which we now call unicorns in the political debate.”

Richard Harrington, who resigned as business minister to oppose the government, said he regretted the situation had come to this. He told Today: “It’s absurd that now we are in a position of political impasse and … parliament hasn’t actually talked about it on the floor of the House of Commons.”

Harrington said he did not think it was likely that the Commons would revoke article 50 and stop Brexit altogether, saying that would probably require a referendum.

“If that were the case then I think it would be very plausible for the prime minister then to say I don’t want this because this is totally different from the last time the public were consulted in the first referendum,” he said.

“Therefore, I feel it would be very legitimate before taking such a dramatic move as revoking article 50 to have another referendum, to see where the public are at.”

Labour’s Hilary Benn, the chair of the Brexit select committee who has been among those pushing for indicative votes, said MPs would vote on a range of Brexit options on Wednesday and then attempt to whittle them down.

“The first time round it will just be ‘here are the propositions’ and you vote for as many as you would like,” he said. “And then we will see the results from Wednesday night. The motion that we will move tomorrow suggests that we go through a similar process next Monday.

“There will obviously be discussions between MPs looking at the results of what has happened on Wednesday night. Which are the most popular options? We may then change the system for next week as we are trying to narrow it down.”

In a statement on his website, Alistair Burt, the third minister to resign on Monday night urged the prime minister to make Wednesday a free vote.

“Parliament should seek urgently to resolve the situation by considering alternatives freely, without the instruction of party whips, and government should adopt any feasible outcome as its own in order to progress matters,” the former foreign office minister said. “I did not believe the government was prepared to do that, so had to vote to ensure this happens.”