Professor Howson, an honorary research fellow at the University of Oxford, said one issue was that schools appeared to be more picky about who they recruited. Acceptance rates are lower for School Direct than for other entry routes, running at about 16 per cent compared with 19 per cent for university-based training.
"They are less willing to take a risk and that is critical if it means the government isn't going to hit its targets," Professor Howson said.
"The government has got to ask itself why these places are not being filled, because the consequence is that there won't be enough new entrants into the profession and schools will be forced to run around trying to plug the gaps."
Professor Howson's research analysed the number of teaching posts being advertised and compared them with figures for students completing initial teacher training. He found that more schools were struggling to fill positions, with more than a quarter of job vacancies in the East and South East of England not resulting in an appointment on the first occasion of advertising.
Although some subjects were meeting their recruitment targets, others were falling far short. If the pattern was repeated this year, he said, it would lead to "a teacher supply crisis of a magnitude not seen since the early 2000s".
Keith Todd, headteacher of Greenway Academy in Horsham, West Sussex, argued that School Direct was contributing to teacher supply problems.
"School Direct has not helped because it is so local," he said. "It only provides trainee teachers for a school or a group, but there are fewer placements from universities for schools which are not using School Direct.
"It's a good idea but the implementation has not been done very well. The schools which don't have a School Direct facility in their area are struggling."
Brian Lightman, general secretary of the Association of School and College Leaders, said the introduction of School Direct had been "patchy", with some schools reporting difficulties in recruiting.
"That might be teething problems in the system or not enough coordination of vacancies. If the number of places is identified centrally but there aren't the applicants in a particular area, that could create a shortage," he said.
A Department for Education spokesman said: "Recent figures show there have never been more people teaching in England's classrooms and there are now more top graduates entering the profession than ever before.
"We have reformed teachers' pay so that heads can reward the most effective teachers.and we have raised the level of bursaries and scholarships available to the brightest maths and science graduates so they are attracted to teaching."
`School Direct is not a magic wand'
Andy Squires, headteacher and teaching school director at Denbigh School in Milton Keynes, says that School Direct has made it easier to develop talent within the school but has not addressed the problems in shortage subjects.
"I don't think it is a magic wand but I don't think it was ever designed to be," he says.
But Mr Squires believes it is understandable if schools are more selective about who they recruit. "Universities are recruiting people for a course, we're recruiting people to stand in front of our students teaching them lessons, and that is a very different perspective," he says. "I don't think schools are risk-averse, I think they generally have higher standards."