Recruitment figures for this year's teacher training courses suggest there will be shortfalls in key subjects.
Another survey said business demand for graduates is up
Postgraduate certificate of education (PGCE) course applications were down 9% so far, Education Data Surveys said.
Maths applications fell from 1,056 to 896, physics from 185 to 129 and ICT from 355 to 297. Only drama, music and social studies saw significant rises.
The Training and Development Agency for Schools said it was too early to draw firm conclusions on these figures.
The main analysis relates to courses in England, but Education Data Surveys said there had been similar falls in applications for courses in both Wales and Scotland.
Prof John Howson, who has monitored these figures for the past 10 years, said that unless the demand for graduates elsewhere in the economy experienced a downturn, it was difficult to see how all teacher training places would be filled this year.
Figures from a survey of major graduate employers last week showed that, on the contrary, vacancies outside teaching were likely to be higher this year.
Prof Howson said: "It may be that graduates now prefer employment-based courses or initiatives such as Teach First, where they can be paid a salary whilst training rather than experiencing yet another year as a student."
Shadow schools minister Nick Gibb said: "It is vital that children get a good grasp of the core subjects like English and maths so they can go on to study further or get the job they want.
"It would be a tragedy if they missed out in the future because of the government's failure to attract enough qualified teachers."
A spokesman for the Training and Development Agency for Schools said it was too early to tell what the final picture would be.
"It is best not to draw conclusions from the first set of figures on applications," he said.
Overall, the trend was "within expectations" and these figures represented "just part of the recruitment picture - they don't include undergraduate numbers or those on employment-based routes", he said.