Schools will have to sack teachers, increase class sizes and drop subjects from the curriculum in the new year because of a squeeze on budgets, head teachers are warning. They predict a "perfect storm", not of their making.

The causes of the schools' financial problems include pay rises, raised national insurance and pension contributions, mounting heating and lighting bills, as well as increased examination costs.

Other expenses hitting classrooms hard include Public Finance Initiative (PFI) repayments on deals signed years ago and increased responsibility for pupils with special needs. Schools are also suffering from cuts to sixth-form budgets, as post-16 education is not covered by the Government's pledge to maintain education spending.

A dossier drawn up by headteachers in Wirral, Merseyside, reveals that almost all of its 22 secondary schools will go into the red within the next two years. Steven Peach, chairman of The Wirral secondary heads' group and headteacher of Oldershaw Academy, said that the financial situation would lead to schools reducing teaching staff and increasing class sizes in 2015.

Brian Lightman, the general secretary of the Association of School and College Leaders, said the plight of Wirral's schools was "absolutely not" unique, adding: "We are very concerned for the prospects for funding for the next couple of years. We have been saying the funding of education post-16 is not sustainable, and now that coincides with increased national insurance payments and the employers' contribution to pensions going up.

"There are also more pupils in the system that we have to educate. We've also been told that any rise in pay wouldn't be funded."

Schools in the North of England were likely to face more hardship than those in the South and London, he warned, but those that would be most affected were schools that have been struggling for some time.

Union leader Brian Lightman says the breadth of the curriculum is at risk (Newsteam)

"We are clear about the extent of the problem. It is our top concern which we have already brought to the attention of ministers – but the fact is we're unlikely to get more funding before the election. I think they understand our difficulties and the level of concern, though," said Mr Lightman.

"We've got to the position where basic provision and front-line services will be cut. It's not only about cutting staffing levels and raising class sizes – they'll have to reduce the breadth of the curriculum. Options won't be offered that have been up until now."

The Wirral heads' dossier says that 19 out of the 22 secondary schools in the borough will be unable to set a balanced budget by 2016/17. A "significant number" will be unable to do so in 2015/16," it added. "It looks likely that for a range of reasons a number of schools are right on the edge of the financial cliff," it states.

Gas and electricity bills, for instance, have risen by £100,000 in the past five years – equivalent to four teaching posts, said Mr Peach. In one year there was a 30 per cent increase. "My big concern is every single head – and we had 19 people at a conference – is facing the same difficulties. It is a perfect storm," he added.

The Wirral heads say they have had "very positive" discussions with the local authority over their financial plight, and plan a further meeting for January. However, they add: "We would welcome support in helping to get the Government to recognise the impact that other financial policies have on schools, in particular the significant increase in national insurance and pensions."

Frank Field, the Labour MP for Birkenhead who has taken up the case of the Wirral heads, said the impact of PFI agreements was particularly "alarming".

He said that companies with whom the agreements were signed were "ripping off schools through maintenance agreements" by levying high charges for repairs. "We've got to find some way of allowing schools to disengage from these contracts. No parent is going to wear teachers being made redundant. It makes a mockery of the pledge to protect education spending."

Russell Hobby, the general secretary of the National Association of Head Teachers, added: "I suspect we're reaching the end of the line for efficiency savings.

"I really do think the past four years have been hard but the fact is we're not reaching the end of the projected cuts. We face as many cuts in the future as we have in past."

He said the decision not to provide extra funding for teachers' pay rises had a significant impact on schools – and that the coalition's pledge to maintain funding had only been kept as a result of the premium for disadvantaged pupils. Schools with few pupils entitled to free school meals were being hit the hardest.

Mr Hobby added that primary schools were also suffering.

A spokesperson for the Department for Education said that school budgets had been protected, with all local authorities receiving the same amount per pupil as in 2010. "At the same time we are providing £390m extra to the least fairly funded areas of the country," he added.

"By April 2015 we will have spent £6.25bn to support disadvantaged children through the pupil premium and build a fairer society." The Wirral, he added, had received more than £46m – above the national average.

A lesson in how to get girls excited about science and technology subjects

Rename them Steam subjects, one teacher suggested in an intervention which could take much of the heat out of the controversy over whether pupils should pursue the arts or sciences. Steam, she argued, as in science, technology, engineering, the arts and mathematics, rather than Stem.

Staff at Malvern St James Girls' School think she has a point. Their belief that Stem subjects can be just as creative as the arts is a key reason why they have bucked the trend and carved out a reputation for their efforts to encourage more girls to study the Stem subjects.

Nationally, only 19 per cent of those who obtain a GCSE Agrade in physics go on to study the subject at A-level. At Malvern St James, a 450-pupil private boarding school in Great Malvern, Worcestershire, 76 per cent of girls at A-level are studying one or more of the Stem subjects and 46per cent studying two or more.

Patricia Woodhouse of Malvern St James (Andrew Fox)

The school's motto is start them young – in fact, start them in Reception lessons where pupils are already getting to grips with the new requirement of the national curriculum to learn aboutalgorithms.

Headteacher Patricia Woodhouse, accepts it may be easier to convince girls of the benefit of studying Stem subjects in a single-sex environment. "I'm not anti-co-ed," she said, "but what we do here is to try to create a liberal environment where the girls are given that opportunity. We're trying to stimulate them and motivate them so they vote with their feet and really enjoy their Stem subjects."

The policy is boosted by a range of out-of-school activities and ambitious work-experience projects. India Wilkinson, a Year 12 student in the first year of GCSEs, did work experience at an animal rehabilitation centre, and Saphia Soros-White is to spend a week on a North Sea oil rig.

The importance of encouraging girls into Stem subjects has been highlighted by Education Secretary Nicky Morgan's backing for the national "Your Life" campaign. This aims for a 50 per cent increase in teenagers opting for A-level maths and physics in the next three years. The current paucity of girls nationally opting for physics showed "too many young people are making choices age 15 which will hold them back for the rest of their lives".

Ms Morgan went on to say of Stem subjects: "They're not stuffy, boring subjects for people who don't get outdoors much – far fromit. They are key, cutting-edge, fast-paced areas of work and they're behind some of the most exciting developments in this country and around the world."

Back at Malvern St James, they would agree: the school has developed close links with local industries. Through involvement with companies such as Morgan Motors, girls have developed an expertise for designing their own motor cars.

One of the innovations helping pupils to gain a deeper knowledge of their subjects is the extended project qualification, which sits alongside A-levels and is quickly gaining wider recognition among universities as a key indicator of a potential student's critical thinking skills. To qualify, a student has to choose a topic to study and give an almost thesis-like presentation of their knowledge.

"It is the enquiring mind that we are trying to develop," said Ms Woodhouse. "It's not just problem solving – it's about stretching the knowledge of the subject. Top universities all say they want evidence of problem-solving and critical-thinking skills."