Theresa May’s personal crusade to expand the number of grammar schools is in serious jeopardy today as senior Tory, Labour and Liberal Democrat MPs unite in an unprecedented cross-party campaign to kill off the prime minister’s flagship education reform.

In a highly unusual move, the Tory former education secretary Nicky Morgan joins forces with her previous Labour shadow Lucy Powell and the Liberal Democrat former deputy prime minister Nick Clegg to condemn the plans as damaging to social mobility, ideologically driven and divisive.

The formation of their cross-party alliance against grammar school expansion, which is opposed by about 30 Tory MPs, spells yet more political trouble for May on the domestic front. Last week, chancellor Philip Hammond was forced by a revolt in his own party into a humiliating budget U-turn over national insurance rises for the self-employed, and Conservatives lined up to oppose planned cuts in school funding.

Launching their combined assault, and plans to work together over coming months, in an article in the Observer, Morgan, Powell and Clegg say the biggest challenges for a country facing Brexit, digitisation and changes to the nature of work, are to boost skills, narrow the attainment gap between disadvantaged children and their peers and boost social mobility. By picking a fight over plans to expand selection in schools, May will, they argue, sow division, divert resources away from where they are needed most and harm the causes she claims to be committed to advancing.

Before a debate in the Commons on social mobility this week, the three MPs say it is time to put aside political differences and fight instead for what is right. “We must rise to the challenge with a new national mission to boost education and social mobility for all,” they write. “That’s why we are putting aside what we disagree on, to come together and to build a cross-party consensus in favour of what works for our children – not what sounds good to politicians.”

In a clear swipe at May, they say: “Those championing selection as the silver bullet for tackling social mobility, or as the panacea for creating good new school places, are misguided.” They add: “While there are positive moves in other areas, such as the new T-levels and opportunity areas, all this good work will be squeezed out by an endless debate about more selection.

Critic: former education secretary Nicky Morgan. Photograph: Daniel Leal-Olivas/AFP/Getty Images

“All the evidence is clear that grammar schools damage social mobility. Whilst they can boost attainment for the already highly gifted, they do nothing for the majority of children, who do not attend them. Indeed, in highly selective areas, children not in grammars do worse than their peers in non-selective areas.

“Having the brightest children in comprehensive schools helps raise standards for all, increasing aspiration and intellectual capital in a school. This isn’t a zero-sum game. As Sir Michael Wilshaw [the former head of Ofsted] has said, he delivered an excellent education for his pupils through the comprehensive system precisely because the school was mixed ability.”

The prime minister has made an expansion of selection her own personal crusade and it is one of her few clear domestic reform plans. But it has run into intense opposition from her own backbenchers, including the Tory chair of the education select committee, Neil Carmichael, and much of the teaching profession.

In the budget 10 days ago, Hammond announced an additional £320m for free schools and grammars, and No 10 insisted that May would press ahead. But with a Commons working majority of 17 – and with the government reeling from the budget fiasco – party whips are aware they will struggle to get the plans through the Commons.

Opponents point out that, as with the Hammond U-turn over national insurance, May’s plans are not in line with the Tory manifesto at the 2015 general election, which made no mention of lifting the ban on new grammars. Conservative critics are privately urging ministers to signal a softening of the policy when a white paper on education reform, expected within the next few weeks, is published.

In their article, Morgan, Powell and Clegg say: “In a time when resources are so limited and many other educational reforms are still in their infancy or yet to be proven – from University Technical Colleges and new T-levels to the expansion of free childcare and hundreds of new free schools – now is not the time for more division or political ideology in education.

“Times have moved on. Expanding selection isn’t part of the answer to tackling social mobility.”