- will add to growing concerns over teacher supply, which has been affected by the introduction of the School Direct training route, the expanding pupil population and an improving economy where graduates are being attracted to other professions.
According to headteachers, the problem is also being exacerbating by workload, high-pressure accountability and "teacherbashing" by the government and Ofsted.
"There have been shortage subjects for a long time but schools are now having much more difficulty, particularly in the core subjects," said Brian Lightman, general secretary of the ASCL. "The situation is intensifying considerably. There is [also] a real difficulty in getting heads of departments in these subjects because of the intense accountability."
The poll of almost 800 headteachers in England and Wales shows that 25 per cent of schools have at least one vacancy in maths, 23 per cent have insufficient numbers of science teachers and 20 per cent are short of English staff.
And headteachers are not just struggling in the core subjects. One in four are finding it hard to recruit staff to teach the new computing curriculum, which became statutory in September, and more than one in 10 are having difficulty filling roles in geography, modern languages and design and technology.
Mark Jackson, headteacher of Haslingden High School in Lancashire, has had a vacancy in RE and one in maths since September, and two of his English teachers are due to leave at the end of this term. "For a permanent RE position I'd usually get 20 applications," he said. "This time I got one. For maths I got two.
"We were struggling all last year to get an English teacher. It took me massively by surprise. Part of the problem is there is that much pressure on English teachers. There is a lot of marking; it is an incredible workload.
"The changes to pay have not changed things very much. We're not a free market where you can pluck a figure from the air to attract people. And if there are not enough English teachers, one school paying more is not going to solve the problem of there not being enough to go around."
Ian Bauckham, headteacher of Bennett Memorial Diocesan School in Tunbridge Wells, Kent, is also chair of the board of the Rochester Diocesan Academy Trust, which oversees three primary schools. He said recruitment problems were affecting primaries as well as secondaries.
"I thought it was only a secondary problem until I discussed it with people in primary phase and said, `It's all right for you in primary', and their jaws fell open. They said it is a nightmare in primary as well, from NQT level to leadership level."
Barrie Scott, headteacher of Cannock Chase High School in Staffordshire, agreed that it was difficult to recruit and retain "high-quality" English, maths and science teachers. "It's not about pay or conditions or pensions. I had a science teacher leave this term who was new to the profession from Teach First. He had great potential but found the workload was impossible. He just said he couldn't go on like this."
Mr Scott said a government strategy, whether regional or national, was needed to ensure that the supply of teachers matched the demand in different subjects.
The poll comes just a month after government statistics on initial teacher training revealed that the School Direct route filled just 61 per cent of the places it was allocated this year. Across all training routes, only 44 per cent of places in design and technology were filled, 67 per cent in physics, 79 per cent in languages and 88 per cent in maths.
Some fear that the rapid introduction of School Direct, which has been assigned 17,609 places for next year, is destabilising teacher supply.
Government statistics for November 2013, the latest available, show that there were 750 vacancies for full-time permanent teachers in state-funded schools and 2,330 temporarily filled posts. By contrast, in November 2010 there were 380 vacant roles and 1,790 temporarily filled positions.
A Department for Education spokesperson said: "It is simply untrue to suggest there is going to be a shortage of teachers. The teacher vacancy rate has remained low at around 1 per cent or below since 2000.
"We always allocate more [training] places than are needed to ensure a high-quality supply of teachers across England's classrooms; we never expect to fill 100 per cent of allocated places and we are confident we will continue to meet future demand."
`The candidates just aren't out there'
Nadine Powrie, headteacher of Fareham Academy in Hampshire, says: "We've had issues with recruiting people for January, particularly in the core subjects of English, maths and science. I'm still looking for a science teacher and an English teacher - both full-time, permanent posts.
"We're a good school, we get good results, but the people just aren't out there. It's very worrying for the future because I'm going to have to be creative with the timetable so the students have somebody in front of them.
"I know many heads are happy to recruit overseas candidates using Skype, but I'm more reluctant to do that because you can't see them teaching.
"There is no doubt it has been more difficult this year. I usually wait until January or February to do recruitment for September, but this year I've started my recruitment campaign early for the core subjects."