Theresa May’s plans to revive grammar schools risk being undermined by government cuts in education funding, after one leading selective school said it was is unable to expand and had asked parents for donations to meet looming deficits.

Parents of pupils at Latymer school, a popular grammar school in Enfield, north London, have been warned that unrelenting financial pressures may mean staff cuts, larger class sizes and fewer subjects for pupils to study at GCSE and A-level.

Latymer’s leadership invited parents to a meeting last week to discuss the school’s “very significant financial shortfall”, with parents urged to make regular donations.

“We are now appealing to all parents and carers of current students to support the school either by making a new or increasing an existing voluntary regular donation,” parents were told in a letter from the school’s headteacher and chair of governors.

“Typically the amount you would pledge would be £30-£50 per month (£360-600 per annum) over the period your child attends Latymer. This averages out at between £1.89 and £3.15 per school day and is considerably less than the average fees of an independent school.”

The financial plight of even successful schools such as Latymer, one of the most over-subscribed in London, suggests grammar schools are looking to retrench rather than expand, as is widely believed by supporters of selective schools.

Founded in 1624 by a city merchant, Latymer is highly sought-after for its excellent exam results and is rated outstanding by Ofsted. But its headteacher, Maureen Cobbett, said grammar schools such as Latymer were subject to the same budget pressures as other state schools.

“We’ve appealed to parents for any support they can give us, and like many other grammar schools we’re appealing to alumni as well, to see if they can offer us any support,” Cobbett said.

The school has been asking parents for voluntary donations for 20 years, and in the past has used the donations to fund new sports facilities and school refurbishment.

“The difference is that we’re saying there’s more urgency this year, because of all the cuts that have affected the school,” Cobbett said.

Expanding the school – suggested by some as a way of increasing the school’s income, and envisaged by the government’s recent green paper as a means of meeting demand for selective schools – isn’t an option.

“If you expand the number of pupils you need more teachers, so it works both ways. We would have considered it, working with the London borough of Enfield, but we are aware that if we expand we would need more buildings, and I don’t think there is any money in Enfield to fund buildings for us,” Cobbett said.

“It’s not always as straightforward as people think – you need more more staff, you need more teachers, you’ve got to pay staff more if they are in charge of a faculty because they have got more work to do.”

Cobbett said that although funding and the government’s efforts to expand grammar schools were “clearly” different, it was funding that was the most pressing issue. “If you ask any headteacher what is concerning them most at the moment, they will say funding for schools and their financial position.

“It’s quite a depressing position to be in for most headteachers – they are facing funding being slashed and yet they are being asked to make standards rise. I don’t see how the two go together,” Cobbett said.

While the government pledged to protect the schools budget from cuts before the last election, increased staffing costs and cuts in funding for 16- to 19-year-olds have seen school budgets shrink in real terms, with little relief in sight other than cost cutting.

With few students eligible for additional funding through the pupil premium top-up or special needs allowances, grammar schools are facing tighter margins than many comprehensive schools.

“The government has claimed that education budgets have stood still – but clearly they haven’t, because of extra costs imposed. They’ve actually gone backwards,” Cobbett said.

“I honestly, hand on heart, can’t see how the government expects state secondary schools – not just grammar schools – to continue to improve standards and to get better results for children, but at the same time impose cuts on our budgets. It just doesn’t make sense. Something’s got to give – and I’m not just talking about Latymer.”

A spokesperson for the Department for Education said: “We want all schools to have access to the resources they need so that every pupil can reach their full potential. We have protected the schools budget so that, as pupil numbers increase, so will the amount of money for our schools – in 2016-17 that will total over £40bn, the highest on record.

“All schools need to manage their finances to deliver the best education for their pupils and to prevent going into debt.”