A pressure group linked to the former Vote Leave campaign has warned Theresa May that signing up to regulatory alignment with the EU to solve the Irish border problem will not allow Britain to “take back control” from Brussels.

Change Britain, which was launched last year with the backing of the foreign secretary, Boris Johnson, and the environment secretary, Michael Gove, made clear its belief that such a move would fail to respect the mandate of the referendum result.

Gisela Stuart, the former Labour MP who led the Vote Leave campaign alongside Johnson and Gove, said: “[It] would be completely unacceptable if we were forced to agree a deal where regulatory alignment saw the UK continue to be subject to rules designed and imposed by Brussels.

“It would be single market membership in all but name. The government must stand firm in the negotiations and stick to the principles set out in the prime minister’s Lancaster House speech.”

The group said May would be signing up to become a “rule taker” if she accepted regulatory alignment in which the UK would have to comply with rules made in Brussels without having elected representatives to oversee the formation and amendment of those laws.

Change Britain said it was not the same as “mutual recognition” of each other’s laws and regulations, which is a different and clearly defined concept in EU trade policy.

Gove and Johnson are not directly involved in Change Britain but the group’s website carries a video of the foreign secretary endorsing its formation. Gove led its policy commission until he became environment secretary.

The group’s intervention comes at a time of increasing unease among senior Conservatives about the prime minister signing up to regulatory alignment as she seeks to solve the problem of the Irish border.

She was prepared to accept the concept in a proposed deal with the EU on Monday but this was vetoed by her political partners in the Democratic Unionist party and senior Tory colleagues have subsequently made clear they are not happy.

They have been further infuriated by May’s apparent attempt to bounce them into the deal, as she did not consult all her cabinet colleagues or the DUP on the exact wording before pressing ahead.

There is particular concern among Brexit-supporting MPs that May is conceding too much to Brussels and there are worries that her No 10 operation has taken too much control over the process to the exclusion of senior leave backers in the cabinet, such as Johnson, Gove, David Davis and Liam Fox.

At the same time, allies of Davis have once again been floating to MPs the idea that he should take over as prime minister – at least as a caretaker leader until the end of Brexit.

However, several newer intake MPs told the Guardian that idea should be given short shrift as the bulk of the party still believes a leadership contest would be a damaging distraction at such a crucial time in the EU negotiations.