Salary supplements such as bonuses should be given to teachers in some subjects to help deal with a growing recruitment and retention crisis, according to a report.

A new study by the Education Policy Institute (EPI) says England is struggling to find and keep enough teachers, particularly in science and maths.

The education secretary, Damian Hinds, has said that making teaching an attractive profession is his top priority.

The report says that a number of factors have put pressure on the teaching workforce in recent years. There has been around a 10% increase in pupil numbers since 2010, while teacher numbers have remained steady, according to EPI’s analysis.

At the same time, teacher training applications are down by around 5%.

“Exit rates” – the numbers leaving the profession – have also increased, the report says, particularly for those in the early stages of their career.

In total, 60% of teachers remained working in state-funded schools five years after starting, the EPI calculates, and for shortage subjects like physics and maths, the five-year retention rate is 50%.

The study also notes that teacher pay has dropped by around 10% in real terms over the last eight years but adds that a recent government announcement of pay rises for teachers of up to 3.5% from next month will halt this decline.

The report says: “The overall teacher labour market in England is in trouble. The squeeze on teacher pay probably had little effect when private sector earnings were also squeezed.

“However, the recent recovery in private sector earnings is making teaching a less attractive financial option for young graduates and is probably behind the negative trends in recruitment and retention in recent years.

“Moreover, the projected growth in pupil numbers means teacher numbers will need to rise in order to prevent class sizes from rising further, rather than staying steady as they have done in recent years.”

Less than half (46%) of secondary school maths teachers and 50% of those teaching physics have a relevant degree, according to the EPI’s analysis of government data.

These are both subjects where there are “significant recruitment and retention problems”, the study says, and graduates in these fields can expect higher average pay in other jobs.

The report says: “The teacher shortage problem appears worse in subjects where graduates can earn most outside of teaching, with persistent problems recruiting and retaining sufficient numbers of physics, maths, chemistry and languages teachers.

“This appears to translate into differences in teacher quality in such subjects, with fewer teachers possessing a relevant degree in the subject they teach.”

The study also notes that shortages of teachers with relevant degrees are worse in deprived areas.

For example, at GCSE-level, outside London, just over a third of maths teachers (37%) and 45% of chemistry teachers at the poorest schools have a relevant degree, compared with 51% of maths teachers and 68% of chemistry teachers working at more affluent schools outside the capital.

The study argues that there is “now a very strong body of evidence from the US that suggests modest salary supplements in maths and science subjects (around 5% of gross salary) can be highly effective in reducing teacher attrition”.

“More generous bonuses (around $20,000-$25,000) have been found to be effective in incentivising existing teachers to move to high-poverty areas,” it adds.

“Schools in England already have the freedom to make such salary supplements, but have been rarely making use of them to date. This is probably because schools would have to self-fund them at a time when school budgets are already severely squeezed.

“We believe that there is a good case for introducing salary supplements in shortage subjects for all early career teachers. To be effective, such a policy would need central funding and direction.”

Report author Luke Sibieta said: “The teacher labour market is suffering from a number of severe shortages, especially with graduates, who are often able to earn much more in other roles.

“Many priority subjects such as maths and science are failing to attract enough highly-qualified professionals. Our research finds that in some parts of England, just one in five physics teachers have a relevant degree.

“There is strong evidence that these pressures can be alleviated by targeted salary supplements. Policy-makers have begun to consider this potential solution, yet so far proposals have been far too modest, and exclude many of the areas most in need.

“The government should therefore roll out a more ambitious scheme, which offers incentives to teachers in a greater number of shortage subjects, covering more areas. This is critical if we are to relieve some of the growing strains in the workforce, and protect pupil outcomes.”

A Department for Education spokeswoman said: “The education secretary has been clear that there are no great schools without great teachers and his top priority is to make sure teaching remains an attractive and fulfilling profession.

“There are still more than 450,000 teachers in our classrooms, 11,900 more than in 2010, and increasing numbers are returning to the profession.

“We recently announced a fully-funded pay rise for classroom teachers and we are working with school leaders and unions on a strategy to drive recruitment and boost retention of teachers and strip away unnecessary workload.

“This is on top of the range of financial incentives we already offer to help attract the brightest and best into our classrooms.”