More than a third of physics teachers do not hold a degree in the subject, official figures show.
In addition, more than a fifth of maths teachers, and almost the same proportion of English staff, hold no higher than an A-level in the disciplines.
Government figures also show that in other core academic subjects, such as chemistry, geography and languages, many children in England's secondary schools are being taught by teachers lacking subject expertise.
School leaders warned that there is a serious shortage of teachers in many subjects, leaving schools no choice but to ask staff to give lessons in subjects in which they do not have a degree.
The data, published by the Department for Education, shows that in November last year, 37.3% of physics teachers held no relevant post A-level qualification in the subject.
An analysis by the Press Association shows that this proportion has risen from 33.7% five years ago.
Among maths teachers, 22.2% did not hold a relevant degree last year, while in English it was 18.6%. These figures have both dropped since 2011.
For the other sciences, last year around a quarter of chemistry teachers (25.1%) held no higher than an A-level in the subject. This is around the same as it was five years ago.
In biology, 9.1% of teachers did not hold a relevant higher qualification, compared with 13.7% in 2011.
Among humanities subjects, the proportion of geography teachers without a relevant post A-level qualification has risen to more than a third (33.8%), compared with 32.5% five years ago, while in history, around a quarter (24.9%) are lacking in subject expertise, down compared with 2011.
For languages, more than a fifth of French teachers (22%), nearly three in 10 German teachers (29%) and almost half of Spanish teachers (47.7%) do not have a degree in their subject. These figures are all down on five years ago.
It may be the case that some languages teachers are native speakers of the languages they teach, but do not have a post A-level qualification in them.
Geoff Barton, general secretary of the Association of School and College Leaders, said: "There is a serious shortage of teachers in many subjects and schools have no choice other than to ask teachers to teach subjects in which they do not have a degree. These staff do an excellent job in difficult circumstances, and may be teaching students lower down the age range.
"However, this is obviously not an ideal situation and we know from practice and research that subject knowledge is a vital ingredient in teaching. Teachers with a degree in their subject are able to draw on a depth and breadth of knowledge, which is hugely beneficial in helping students to understand and master the subject."
"The solution is simple: we need more teachers."
Mr Barton said the Government must do more to make teaching an attractive career and to ensure people stay in the profession.
ASCL is keen to work with the Government to address the issue, he said.