The leader of the backbench Conservatives at Westminster has raised serious concerns about plans to force all state schools to become academies by 2022, in a blow to government hopes of forcing them on to the statute book.

In a sign of the depth of Tory unrest, Graham Brady, chairman of the 1922 committee, said the plans announced by George Osborne could lead to the creation of “new and distant bureaucracies” rather than delivering greater freedom and autonomy for schools. He also said they could have the unwelcome effect of removing parents from governing bodies and reducing accountability.

Brady, who spoke out as new data suggested the reorganisation could cost more than £1.3bn, is writing to education secretary Nicky Morgan in the hope that the proposals spelled out in the recent education white paper can be changed. He also wants reassurances from Morgan that the plans will not be rushed through parliament – suggesting that without a rethink they could trigger a backbench Tory rebellion.

The intervention by such a senior figure is a serious setback for Morgan, who insisted only last weekend there would be no rethink or U-turn despite uproar among Conservatives in local councils, who are furious that their authorities are to be stripped of any role in running schools, even in areas where they have been successful. On Saturday, it emerged that another Tory MP, James Cartlidge, the member for Suffolk South, had raised his concerns with ministers about the plans and now also intends to tackle Morgan on the issue.

Tory councillors have united with Labour and Liberal Democrat counterparts to form a cross-party alliance in opposition to the plans. They complain that a costly and disruptive reorganisation will be forced on parents and teachers. The vast majority of the schools affected will be primaries, most already judged good or outstanding by Ofsted.

Brady said that he was worried that new academy chains would become too big and unaccountable. “I’ve always favoured greater autonomy for schools. But I do think there is an issue if all schools are to become part of huge new chains, in which there is little accountability or parental involvement,” he said.

In a letter to a constituent, which was posted on Twitter, Brady said: “If this move happens in the wrong way, there is a danger that instead of more freedom for schools we might see new and distant bureaucracies springing up.” He added: “I hope there will be an opportunity for proper consideration of and improvement of the government’s proposals.”

On Friday night the row escalated as new parliamentary answers provided by the minister for children and families, Edward Timpson, suggested ministers face a £1bn-plus funding “black hole” to pay for the plans. In answer to a question by Labour MP Jess Phillips about how much the Department for Education had already spent on converting schools to academies, Timpson revealed that the total bill for converting 4,897 schools has been £323m since 2010.

This works out at an average cost per school of just under £66,000. Were the average cost to remain the same, the bill for converting the remaining 16,800 schools would be more than £1.1bn. Only £140m was announced to fund the plans in Osborne’s March budget.

All local authorities will also face large bills for forced academisation with no compensation from central government. Staffordshire county council has estimated that the average cost to the council of converting a school to an academy is £12,300, including legal fees and other necessary changes, such as transferring land, IT systems and records.

Timpson revealed in a separate written answer that the average time taken for a maintained school to convert to an academy is seven months, a process that teaching unions says causes huge disruption to teachers, pupils and parents.

Labour said the entire process would harm rather than improve schools. Shadow education secretary Lucy Powell said: “Schools are facing huge challenges over this parliament, including falling budgets for the first time since the mid-1990s, which will mean fewer teachers and teaching assistants. This costly reorganisation is an unnecessary and unfounded distraction, which could harm standards.

“These new figures show the real cost of this reorganisation and lead me to ask, yet again, why? Schools don’t need this, parents, communities, teachers and school leaders don’t want it, and now we find that it’s going to cost over £1bn, money which could be better spent driving up standards.”

A Department for Education spokesperson hit back at claims that the plans were underfunded, saying: “It is untrue to suggest there will be a shortfall of funding for our academisation plans. As set out in the spending review, and in last month’s budget, we have enough funding to support a high-quality, fully academised school system. We have over £500m available in this parliament to build capacity in the system – including recruiting excellent sponsors and encouraging the development of strong multi-academy trusts.”

But Labour insisted that, of the £640m in the budget red book, £500m had been set aside for the separate transition to a fairer funding formula for schools, leaving ministers with a funding “black hole” of more than £1bn over the next six years.