Grammar schools are considering asking parents for cash to make up budget shortfalls set to be caused by changes in funding, head teachers have warned.
Families could be asked for £30 to £40 a month to ensure teaching standards do not fall, the Grammar School Heads Association (GSHA) has said.
Conservative MPs have called for the Government to review the "unacceptable" reforms, which could leave some schools choosing between cutting facilities or switching off heating to keep costs down.
Tim Gartside, head of Altrincham Grammar School for Boys and a member of the GSHA, said he was considering asking parents for hundreds of pounds a year in voluntary contributions and many others were considering similar plans.
He told BBC Radio 4's Today programme: "We have a choice, I suppose. Either reduce the curriculum, increase the class size or go to parents and say we need to ask you for a contribution in order to be able to make the school operate as it has done before."
The proposed new national funding formula announced by Education Secretary Justine Greening in December increases money targeted at schools with additional needs, including deprivation.
The changes, to be introduced from 2018 to 2019, will mean more than 10,000 schools gaining funding, it has been suggested.
But unions warned earlier this month that 98% of schools face a real-terms reduction, with an average loss of £339 per primary pupil and £477 for secondary students.
The GSHA said 60 grammar schools will gain under the changes but 103 will lose money. It said the majority of grammar schools are already receiving below the level considered viable for running a school.
Conservative Fiona Bruce told Today: "All my senior school head teachers and many of my junior heads are saying that the way this formula is calculated will leave them with no choice but to actually effectively reduce teaching standards in their schools."
The Congleton MP said schools were looking at leaving teaching posts vacant, reducing curriculum options, closing sixth forms and special needs units, and switching off the heating as ways of saving money.
"This is unacceptable, this is not fair funding."
Free schools have also warned the reforms mean they face adopting a four-day week, scrapping sixth forms or cutting arts subjects from the syllabus.
Sarah Burns, Sandbach Boys School head teacher, told the programme: "They are absolutely realistic possibilities given the level of cuts and the fact that we've already cut to the bone.
"Given those levels of cuts we will have to take some really hard decisions like those."
A Department for Education spokesman said: "The Government has protected the core schools budget in real terms since 2010, but the system for distributing that funding across the country is unfair, opaque and outdated.
"It is based on patchy and inconsistent decisions that have built up over many years and on data that is over a decade old.
"We are going to end the historic post code lottery in school funding.
"Under the proposed national schools funding formula, more than half of England's schools will receive a cash boost in 2018-19.
"This will help to create a system that funds schools according to the needs of their pupils rather than their postcode.
"Funding every child fairly and according to their specific needs sits at the heart of delivering the Government's pledge to build a country that works for everyone, not just the privileged few.
"We recognise that schools are facing cost pressures, which is why we will continue to provide advice and support to help them use their funding in cost effective ways, including improving the way they buy goods and services, so? they get the best possible value for their pupils."