The universities minister, Sam Gyimah, has resigned in protest at the prime minister’s Brexit plan and pledged to vote against the agreement in parliament. On Friday, he became the seventh minister to quit Theresa May’s government over the issue.

Gyimah said the deal on offer would mean the UK lost its voice in the European Union, while still having to abide by the bloc’s rules.

“In these protracted negotiations, our interests will be repeatedly and permanently hammered by the EU27 for many years to come. Britain will end up worse off, transformed from rule makers into rule takers,” he wrote in an article for the Daily Telegraph.

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“It has become increasingly clear to me that the proposed deal is not in the British national interest, and that to vote for this deal is to set ourselves up for failure. We will be losing, not taking control of our national destiny.”

And the Conservative MP for East Surrey, who voted to remain in the EU, said May should not rule out holding a second referendum.

Sam Gyimah MP (@SamGyimah) After careful reflection, I will not be supporting the Government on the EU Withdrawal Agreement. As such, I have tended my resignation as Universities & Science Minister – read more on my Facebook page: https://t.co/EFQrBjkJZG

The resignation is a fresh blow to the prime minister, who has been trying to get on the front foot in the fight to force her deal through parliament on 11 December.

The Democratic Unionist party, which struck a confidence and supply deal with the Tories after the last election and upon whom May relies heavily, has already indicated it would not support her plan. And many of her own MPs, as well as the Labour party, do not back it either.

Gyimah’s resignation triggered an outpouring of support from Tory remainers, including two former ministers, who highlighted his suggestion that a second referendum was an idea worth considering now May’s deal had been made public.

Jo Johnson, who quit from his job as rail minister over Brexit earlier this month, said Gyimah’s resignation was “strong and principled” and welcomed his openness to “giving the public the final say”.

The former education secretary and leading supporter of the campaign for a second referendum Justine Greening said: “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.”

She was backed by the Lib Dems’ education spokesperson, Layla Moran, who said Gyimah’s resignation was yet more evidence the prime minister did not have the support of parliament. “The list of Tory rebels for May’s deal gets longer and longer and she is now searching for a new universities minister as well as votes. This government is falling apart and the decision must be taken back to the public.”

Earlier this week, Gyimah was spotted at a breakfast meeting in Westminster with Johnson and the soft Brexit-supporting ministers, Greg Clark, David Gauke and Margot James, prompting speculation about plotting by those on the left of the party.

With speculation about further resignations swirling on Friday night, James swiftly declared she was not going to quit, saying: “I fully intend to support the deal the PM is putting to parliament on 11 December.”

Gyimah is likely to join the People’s Vote second referendum campaign, after talking to Johnson and Greening in the run up to his departure. But, with the ink barely dry on his resignation letter, he has yet to decide precisely what he intends to do.

Chief among his concerns was the protracted negotiations over Galileo, the EU’s strategic satellite navigation system. The government has said UK defence and security services would no longer participate after Brexit and it emerged on Friday that the country may never claw back £1.2bn it had already invested.

Gyimah said the prime minister was right to withdraw from the negotiation, which he said was “stacked against us from the very beginning”. But he added: “Galileo is only a foretaste of what’s to come under the government’s Brexit deal.”

He wrote: “There is a mountain to climb, and we are still in the foothills. Under the deal we will have only two, at most four, years to agree at least five times what has been settled to date.

“With so much left to negotiate, we must take a clear-eyed view on the strength of our position.” Gyimah said the EU had held the cards so far in the negotiations and time was not on the UK’s side. “All of this points to an off-the-shelf deal dictated by the EU that will be materially worse for my constituents in East Surrey than staying in.”