School budgets face cuts to fund a new teachers’ pay rise after the government announced it would only partially fund the award of 2.75%.

Teachers are among almost a million public-sector workers – including hospital doctors and soldiers – who are to receive above-inflation pay rises for a second year in succession.

The increases – which follow the recommendations of independent pay review bodies – are backdated to the start of the financial year and include 2.5% for consultants and dentists, 2.5% for police officers, 2.9% for armed forces personnel, at least 2.2% for prison officers, and 2% for senior civil servants and senior military staff.

But the award for teachers is equivalent to a £1,000 increase on average classroom pay, and the government was accused of achieving the “worst of all worlds” by school leaders, who said schools could not afford to deliver a “derisory” pay settlement.

Only 0.75% is being funded by the government, which has deemed the remaining 2% “affordable”.

Geoff Barton, the general secretary of the Association of School and College Leaders, said: “It is inevitable that this will result in more cutbacks, and while schools will do their best to implement the increase, we would not be surprised if some are unable to do so.”

The National Association of Head Teachers (NAHT), which represents leaders in the majority of schools in England, described it as a missed opportunity to begin to solve the staffing crisis in schools and colleges.

“Unfortunately, leaders will have to cut elsewhere in their budgets in order to find the money needed to fund even this moderate rise,” said Paul Whiteman, the NAHT’s general secretary.

Schools will continue to determine how staff are paid but the pay increase will be supported by an additional £105m to be paid through the teachers’ pay grant, said the Department for Education, on top of £321m already committed for the 2019-20 financial year.

The education secretary, Damian Hinds, said: “Today’s announcement of a 2.75% pay rise for teachers, accepting the STRB’s [School Teachers’ Review Body’s] recommendations in full, means that teachers and heads can receive a pay rise above current rates of inflation and have more money in their pockets.

“If we want the best people working in our classrooms then it’s right that we ensure their salaries recognise the vital nature of their work and the potentially life-changing impact they can have on the lives of our children.”

His department said the pay award meant the minimum starting salary for a qualified teacher in 2019-20 would rise from £23,720 to £24,373 outside London and from £29,664 to £30,480 in inner London.

Angela Rayner, the shadow education secretary, said the announcement would not reverse nearly a decade of real-terms pay cuts for teachers and school support staff.

“This announcement has been made after schools have submitted their budgets for next year, and school leaders and teachers continue to face destabilising uncertainty about their budgets in the years ahead.”

The Liberal Democrats’ education spokeswoman, Layla Moran, said headteachers would now have to decide which support staff to sack or which basic supplies to cut back.

“No headteacher should have to make these sorts of decisions – schools should be fully funded and teachers should be paid properly.”

Confirming the awards across the public sector, the chancellor, Philip Hammond, said they had been made possible by the work done to rebuild public finances.

While hospital doctors will get an average of £1,500, an army corporal on average wages will get an additional £995 while police constables will get up to £978 more.

Public sector pay rises – who gets what?

Schoolteachers 2.75%

Equivalent to a £1,000 increase to average classroom teacher pay and a £1,620 increase in the average pay of school leaders.

Consultants and dentists 2.5%

Ranges from £970 and £1,820 for specialty doctors through to £1,940 and £2,630 for consultants.

Police officers 2.5%

The Police Federation said the pay rise equates to about an extra £1,000 of pensionable salary a year for a constable.

Armed forces personnel 2.9%

The lowest-paid soldiers, sailors and airmen and women will receive a 6% increase to bring them in line with the living wage. It means new and junior personnel will receive a £20,000 salary while an officer’s starting salary will rise by £769.

Prison officers 2.2%

There will be a targeted 3% increase for band 3 officers on new terms and conditions as part of moves to reduce the gap with those on older conditions.

Senior civil servants and senior military staff 2%

Exceptions that include limiting the overall figure to an average 2% increase will mean a lot less for most members of the senior civil servants’ union, the FDA.