Headteachers have insisted that expanding the number of grammar schools would do nothing to increase social mobility or lift standards of education, as they demanded that Theresa May consult them urgently before legislating to expand selection.

After the chancellor, Philip Hammond, announced an additional £320m for free schools and grammars in his budget last Wednesday, teachers and some Tory MPs reacted with alarm at the haste with which ministers are pressing ahead with plans to end the ban on new selective schools.

On Friday, education secretary Justine Greening was jeered at the annual conference of the Association of School and College Leaders (ASCL) as she attempted to defend the plans. Speaking from the conference, the interim general secretary of ASCL, Malcolm Trobe, who was a headteacher for 17 years, said it was vital that heads were consulted by ministers before they fixed their ideas in stone and took the wrong track.

“People who work in grammars do a very good job, but there is no evidence that increasing the amount of selection will increase social mobility or the overall education standards across the country,” Trobe said. “Therefore we believe that increasing the number of selective schools should not happen. Do not increase selection because the evidence base is that it will not have the desired effect.”

In their response to a written consultation on the issue, the ASCL told the government that there was also concern that taking brighter pupils out of comprehensives would have a detrimental effect on those schools, and therefore harm the education of the vast majority of pupils.

Trobe added: “We are waiting to hear the response to our comments. What we say is we want to be engaged in the process before it gets to publication of the white paper. This is a very important issue, and big issues need a long-term strategy and a significant amount of discussion before anything comes out of it.”

With Brexit due to dominate parliamentary business over the next two years, an education bill to end the ban on selection is one of the few domestic bills that Tory MPs believe will be advanced in the next session of parliament. But many now fear the plans – opposed by at least 30 Conservative MPs – will run into trouble.

The Tory MP and former government minister Dan Poulter said it was important that the government acted on the basis of evidence: “The government is right to invest in the next generation and to look at ways to improve the life chances and opportunities of younger people.

A report in the Times claimed grammar schools were going to lower entry test marks for poorer children. Photograph: Christopher Furlong/Getty Images

“However, it is important that changes to the school system are properly evidence-based, and that improving social mobility and the opportunities available to children from disadvantaged backgrounds are front and centre of any future plans.”

A report in the Times saying that grammar schools were to lower entry test pass marks for poorer pupils, in order to increase the intake of pupils from poor backgrounds, was described as “speculation” by the Department for Education. Reacting to the claims, Robert McCartney, chairman of the National Grammar Schools Association, said such a measure would further disadvantage poorer pupils in the long term, by leaving them unable to compete with more privileged students who had been coached.

“How are children from these areas going to compete in these tests against middle-class children with a number of advantages from private coaching to domestic circumstances? The answer is, they’re not. The government is trying, for I think political reasons, to give the impression that, if they are forced to take more disadvantaged children at a lower level of entry, this would somehow be a cure.”

Government figures released last week revealed that just 2.6% of grammar school pupils were eligible for free school meals, compared with 11.6% of secondary modern pupils and 14.1% of pupils across all secondary schools.

The extra money for free schools and grammars, and an injection of an extra £2bn into social care, were supposed to catch the most attention in the Hammond budget. But instead the reaction was dominated by a revolt over a proposed rise in national insurance contributions for the self-employed.

Around 20 Tories, including Wales minister Guto Bebb, have raised concerns about the changes, which have now been delayed until the autumn. It emerged on Saturday night that Hammond has asked foreign secretary Boris Johnson to speak out in the Commons on Monday in support of the Budget. Sources said the arrangement had been made before the budget was delivered.