Sam Gyimah, the universities minister who resigned in protest at the prime minister’s Brexit plan and pledged to vote against it, has said a second referendum could be the most sensible path for both leave and remain supporters, and dismissed Theresa May’s agreement with Brussels as a “deal in name only”.

The Conservative MP, who on Friday became the seventh minister to quit Theresa May’s government over Brexit, called for a vote to gauge the public’s mood if May loses the meaningful vote in parliament on 11 December.

He said the deal May had brokered with the European Union would “cripple our interests for decades to come” and a second referendum could avert “chaos”.

Sam Gyimah. Photograph: Conservative party/PA

“There is a blocking minority in the House of Commons for almost every possible option which means that letting the people decide, now that we know more, might be the most sensible path for both leavers and remainers,” Gyimah told the BBC Radio 4 Today programme on Saturday.

“The prime minister has already taken one step in that direction by appealing to the country to put pressure on MPs to vote for her deal.

“If you are going to appeal to the country to put pressure on MPs to vote for a deal, then by all means you can give the decision to the country in terms of which direction we go in. If parliament was in deadlock, Theresa May could get herself out of that deadlock by backing a second referendum.”

Gyimah, who voted to remain in the EU in 2016, likened the negotiations to a football match in which the opposition “are the referee and they can make up the rules as they go along”.

He added: “We all know more about the EU than we did during the first referendum and in particular the terms of our departure. I am happy to concede if we have a second referendum and if leave wins, at least we would do it with our eyes wide open.”

The MP for East Surrey said he came to his decision after looking through the terms of the deal and receiving feedback from his constituents.

He also cited May’s decision to give up on efforts to gain access to the EU’s Galileo satellite navigation system for defence and critical national infrastructure purposes after being frozen out by Brussels, which he has said was “a foretaste of the brutal negotiations we will go through that will weaken our national interest, make us poorer, less secure.”

“We don’t actually have a deal, we have a deal in name only,” Gyimah said. “What we have is a series of principles of what we want to achieve as a country, a set of negotiations after we have left the EU and given up our voice, our veto and our vote.

“Our interest will be hammered during these negotiations, we have no leverage. They [the EU] set the hurdles you have to clear.

“We will have to deal with these consequences and the public would not forgive us if we don’t level with them on the difficult choices ahead.”

Gyimah’s departure highlights the scale of the task facing May if she is to avoid a potentially crippling defeat in the Commons.

The Democratic Unionist party, which has a confidence and supply deal with the Tories, has indicated it will not support May’s plan, as has the Labour party and many of the prime minister’s own MPs.

Jo Johnson and Justine Greening, two former ministers, welcomed Gyimah’s suggestion that a second referendum was worth considering now May’s deal had been made public.

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“Like many MPs, he has recognised the huge shortcomings of the prime minister’s deal and the need to find an alternative path forward for Britain,” said Greening, a leading supporter of the People’s Vote campaign.

However, the culture secretary, Jeremy Wright, said he was sad to see Gyimah leave the government over Brexit.

Wright acknowledged the agreement with the EU was not perfect, but said he believed it was the best one available.

“All of my colleagues are going to have to make their own judgment about what they think about this deal,” he told the Today programme.

“The negotiation we have had with the European Union was always going to be a matter of compromise for both sides. You do have to compare this deal with the realistically available alternatives.

“Either we leave with no deal, which would have serious economic consequences, or we say to the British public: ‘I’m sorry you have got it wrong, you are going to have to do it again’, which I think would have serious democratic consequences.”

Michael Gove – one of the leaders of the leave campaign – urged Tory Brexiters to get behind the agreement. In an article for the Daily Mail, he warned that Brexit could be “in peril” if the agreement was voted down.

“Does the deal deliver 100% of what I wanted? No. But then we didn’t win 100% of the vote … you can’t always get everything that you want,” he said.