More than one in four local authority maintained secondary schools in England are in the red, with an average deficit of more than half a million pounds, while many more are “teetering on the edge”, according to new financial analysis.

Though there has been a slight improvement on last year’s figures with marginally fewer secondaries now in deficit, research by the independent Reform thinktank shows the financial health of many of England’s schools remains fragile. Headteachers have had to make staff redundancies, increase class sizes and even shorten the school week to save money.

The study focusses on schools under local authority control and therefore does not include academies and free schools, but the numbers are still significant and provide an insight into the struggle many headteachers face trying to make ends meet.

Reform found that since 2010-11, the proportion of local authority-funded secondary schools with no cash reserves has almost doubled to 28.3%, with the average deficit now up to around £570,000. Yorkshire & the Humber and the South West are the worst affected with 38% in deficit.

The proportion of primary schools in deficit is much smaller at 8%, having increased by 2.1 percentage points over the same period.

The research also highlights “drastic” variations between schools. While many have struggled to stay in the black as a result of an 8% real-terms cut in per-pupil funding since 2011, 36% of secondaries have an “excessive surplus” of cash in the bank – on average more than £390,000.

The new government has promised an extra £4.4bn a year for schools until 2022-23, with a commitment to level up funding to bring primary schools up to a minimum of around £4,000 a year, and secondaries up to £5,000.

Report author Dr Luke Heselwood called however for better targeting of money. “Extra cash for schools is welcome, but it must be well spent. A universal ‘levelling-up’ approach risks wasting taxpayer’s money, while failing to sufficiently help those schools in financial hardship.”

Former headteacher Geoff Barton, who is general secretary of the Association of School and College Leaders, said even where schools have money in the bank it is likely to be diminishing at a rate of knots because of funding pressures.

“The government has allocated additional funding for schools over the next three years but this will not be enough to reverse all the cuts that have taken place and the financial situation will continue to be challenging for the foreseeable future.”

The new government will outline its policy priorities in the Queen’s speech on Thursday. Kevin Courtney, joint general secretary of the National Education Union (NEU), warned: “Under current government funding plans it is a simple truth that 83% of schools will be worse off in April 2020 than in 2015 in real terms.”

Commenting on the research, the Department for Education said it would be “retrograde and unfair” to direct funding to schools based on their historic spending decisions.

“This government has announced the biggest funding boost for schools in a decade, giving every school more money for every child. This means that every school in the country can see per-pupil funding rise in line with inflation next year, with all secondary schools receiving a minimum of £5,000 per pupil.”