Nearly two in five physics teachers do not have a degree in the science, according to new figures.
Official data indicates that in many key academic subjects, pupils are increasingly being taught by staff that are not specialists in the area.
The figures also show an overall dip in the number of teachers working in England's schools, sparking fresh warnings about a "recruitment and retention crisis".
School leaders urged the Government to take action as "a matter of urgency".
The statistics, published by the Department for Education (DfE), show that in 2017, 38% - almost two in five - of physics teachers in England did not have a relevant post A-level qualification.
This is up from 37.3% in 2016.
Physics has the largest proportion of teachers without a relevant degree, among English Baccalaureate subjects, the data shows.
In addition, a third (33.3%) of geography teachers do not have a relevant post A-level qualification - this is down slightly on the year before.
Around a quarter of history teachers (25.3%) and the same proportion of chemistry teachers (25.3%) do not have a degree in their subject.
The subjects with the highest percentages of teachers holding relevant post A-level qualifications include English (81.2%), biology (90.5%), combined sciences (90.1%) and other sciences (84.5%).
More than three in four (78%) maths teachers have a relevant post A-level qualification, the figures show.
Geoff Barton, general secretary of the Association of School and College Leaders, said: "Schools already frequently have to use teachers who don't have a post A-level qualification in the subject they are teaching because of the severe difficulties in recruiting staff.
"The fact that today's census shows that the percentage of non-specialists has increased in some of the English Baccalaureate subjects is therefore no surprise. These teachers often do a great job but it is far from an ideal situation and parents will rightly want their children taught by teachers who are specialists in their subjects."
A DfE spokesman said the Government is offering bursaries and other financial incentives to encourage would-be teachers to train in key subjects such as maths and physics.
The latest figures show that overall, the equivalent of 451,900 full-time teachers were working in England's state schools as of last November - down from a peak of 457,200 the year before, a drop of 1.2%.
Primary and nursery teacher numbers fell by 0.6%, the data reveals, while secondary school numbers fell by 1.9%.
Mr Barton said: "We are already in the midst of a long-running teacher recruitment and retention crisis and this is set to worsen unless action is taken as a matter of urgency.
"The number of pupils in our schools is set to rise by about 500,000 over the next five or six years and unless we can attract more people into the teaching profession, and retain them, it is hard to see how schools will be able to put teachers in front of classes.
"This situation represents a serious threat to educational standards, particularly in schools in areas of high disadvantage where it is often most difficult to recruit teachers."
He added: "The Government spent too long in a state of denial about this situation and, having finally woken up to the problem, has simply not done enough to address it."
Paul Whiteman, general secretary of the National Association of Head Teachers, said: "We must have a national strategy for teacher recruitment, otherwise schools will never be able to guarantee enough high-calibre teachers for every class.
"We also need to address the root causes of the problem which sees too few new recruits entering the system and too many experienced hands leaving prematurely.
"Teacher recruitment is a pipeline that is leaking at both ends. Paying teachers properly for the essential work they do, not overloading them with work, and giving them access to proper professional development throughout their careers are the key steps that the Government needs to take.
"And they need to do it fast."
A DfE spokesman said: "The number of teachers in our schools remains high, with more than 450,000 in classrooms across the country. An additional 32,000 trainee teachers were recruited last year, despite an extremely competitive graduate labour market which shows that teaching continues to be an attractive career.
"Teacher recruitment will always be challenging in a strong economy with record numbers of jobs.
"But we know there is more to do which is why the Education Secretary has made it his top priority to make sure teaching remains an attractive and fulfilling profession.
"We are building on our strategy to drive recruitment and boost retention of teachers, working with the unions and professional bodies, and pledged to strip away workload that doesn't add value in the classroom."