Schools in England face further strains on their budgets unless the government acts to fill a £1.7bn pension black hole, according to parliamentary research.

The figures, compiled by the House of Commons library and released by Labour, suggest that increased pension contributions for state sector staff could run to £4bn for the government as a whole, of which schools would face having to pay up to nearly £1.7bn by the end of the current parliament.

While the Department for Education (DfE) is to receive extra funding to meet the higher contributions for the first year, Peter Dowd, shadow chief secretary to the Treasury, said the government should commit to paying the extra pensions costs in the spending review.

“These cuts are the equivalent of paying the salaries of nearly 22,000 teachers – staff whom we desperately need after eight years of crushing austerity in education,” said Dowd. “The chancellor must immediately own up and commit to meeting these extra costs, not just push them on to struggling schools, whose budgets have already been slashed.”

The government’s announcement came late last week, and would be the second time in recent years that school budgets have had to absorb unfunded pension increases.

The House of Commons calculations anticipate that pension costs for state schools will increase by £830m a year, after a potential 7% increase in employers’ contributions. The calculation is based on new rules announced last month by the Treasury for the valuation of public service pension schemes.

The increase is also expected to hit a large number of universities in England and Wales whose staff are members of the teachers’ pension scheme. Pension schemes for the NHS and local government are also likely to be affected.

“Theresa May told us that austerity is over, but now it looks as though the Tories are sharpening the knife for more,” said Dowd.

Labour’s claim came as May and Jeremy Corbyn clashed at the dispatch box over the government’s record on education, after the DfE was reprimanded earlier this week for its misuse of statistics by the UK statistics watchdog.

May told MPs: “We now see 1.9 million children in good and outstanding schools compared with 2010, and part of that is based on the reforms we’ve put forward.” However, earlier in the week, the chair of the UK statistics authority, Sir David Norgrove, had told the DfE that the 1.9 million figure “does not give a full picture”.

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The government remains under pressure over school funding ahead of the spending review on 29 October after a Whitehall protest by headteachers at the end of last month attracted wide publicity.

A letter from headteachers, backed by the WorthLess campaign group lobbying for improved school funding, thanked parents for their “overwhelming support” for the protest.

According to the Institute for Fiscal Studies, total school spending per pupil in England has fallen by about 8% in real terms between 2009-10 and 2017-18, once rising pupils numbers and cuts to sixth-form and local authority funding are taken into account.

A DfE spokesperson said: “The changes to the public sector pension scheme will mean better benefits for teachers and staff working throughout our education system – on top of what is already one of the best pension schemes available in the country.

“We have already made clear that we intend to provide funding for state-funded schools and further education colleges for the additional costs in 2019-20, and we will be consulting on this shortly to ensure that our proposed approach is the right one.”