The government has announced £400m investment to repair school and college buildings in England, but the money will only be available to academies that can demonstrate pay restraint on executive salaries.

Academies and sixth form colleges have been invited to bid for a share of the money which can be used to replace roofs, upgrade sports halls or science labs, and deal with general wear and tear in ageing school buildings.

But as schools continue to struggle to balance their budgets in the face of funding cuts, ministers are concerned that too many executives in multi-academy trusts are still paying themselves excessive salaries.

Now the government has warned that any trusts where a single executive is paid more than £150,000, or there are two employees taking home in excess of £100,000 each, will be penalised in the case of an application for building repair money, and an award will be less likely.

Since 2017, the government has challenged 278 academy trusts over excessive chief executive pay, but the Department for Education confirmed that fewer than a fifth (51 in total) have reduced top salaries as a result.

Teaching unions condemned the money available as woefully inadequate. In 2017, the National Audit Office calculated that it would cost £6.7bn to return England’s schools to a satisfactory condition or better.

Two years on the cost is likely to be even higher, said Mary Bousted, joint general secretary of the National Education Union. “This is simply far too little, far too late and it is unacceptable that, in the 21st century, so many children and young people go to schools which have Victorian conditions.”

Bousted said government attempts to link funding to pay restraint only underlined ministers’ failure to address excessive pay in the academy sector. Although minsters may preach pay restraint, they have no levers to pull to make it happen, she said.

The annual condition improvement fund (CIF) is open to smaller academy trusts and sixth form colleges to fund building repairs and improvements. It also pays for a small proportion of expansion projects, for institutions rated good or outstanding by Ofsted. It is one of a number of streams of capital funding available to different types of schools.

The CIF announcement was made days before the deadline for parents to apply for a secondary school place for their child this Thursday. Councils have warned of a looming crisis as a population bulge moves from primary into secondary, increasing demand for places.

The government insists, however, that it is on track to create a million new school places this decade and says this year 93% of parents received offers for one of their top three choices of secondary school.

Gavin Williamson, education secretary, said: “This government is determined to give all children the best possible education, but as well as great teachers, we want all pupils to learn in classrooms that enable them to gain the knowledge and skills they need for success.”

The DfE said bids for CIF funding would be assessed on a points-based criteria. Applicants will get a four-point deduction if they pay excessive executive salaries or have not submitted a financial improvement plan. An extra point will be available to those that have signed-up to the most recent government funding agreement.

Geoff Barton, general secretary of the Association of School and College Leaders, said any additional funding for education was welcome, but dismissed the latest announcement as “hype” rather than proper investment.

“The various strings attached – such as linking proposed funding to type of institution rather than to places of greatest local need – is deeply misguided, as is making allocations dependent on some assumed notion of individual pay restraint.

“The NAO couldn’t be clearer about the woeful neglect of too many of Britain’s schools and colleges. This announcement shows a failure by government both to grasp the urgency of the issue and the need to put fairness before ideology in tackling it”.

School funding is likely to be a key battlefield in a general election. Boris Johnson’s government has announced plans to put more money into schools, starting in 2020-21 and continuing until 2022-23, when it says an additional £7bn will be spent. Unions say the extra money is not enough to reverse the cuts and the funding crisis is far from over.