Teacher shortages in England are growing and the government has missed recruitment targets for four years, the official spending watchdog has said.
It means 28% of secondary physics lessons are taught by teachers with no more than an A-level in the subject, the National Audit Office report says.
Ministers have a "weak understanding" of local teacher shortages, it adds.
The government said overall teacher numbers had risen and blamed unions for "talking down" the profession.
While the overall number of teachers has kept pace with rising pupil numbers, teacher shortages are growing, particularly in poorer areas and at secondary level, according to the authors.
More than half (54%) of head teachers in schools with large proportions of disadvantaged pupils find attracting and keeping good teachers is "a major problem", compared with a third (33%) of those in other schools, they found.
The Department for Education "has a weak understanding of the extent of local teacher supply shortages and whether they are being resolved", the report said.
"The department takes a national approach to recruitment but has more to do to understand important local and regional issues."
Voice from the frontline
Anonymous head teacher
The teacher shortage is acute, and the government needs to accept this.
I am head teacher of a large, oversubscribed, high attaining primary school and I cannot get staff. I am not getting a single applicant for jobs - not one.
I have several agency staff working in my school, all of whom are very expensive and many of whom only wish to work part time so I have classes with job share teachers.
I am not able to pick and choose my own staff at interview, because there are no interviews, so I am reliant on agencies to supply teachers of a reasonable quality. For my last two jobs they have been unable to do this.
The situation is dire and getting worse. Ultimately it is the children who suffer as we do not have the quality of teachers they deserve.
It is totally infuriating and demoralising to hear the government keep repeating that there is no crisis.
Come and visit my school, and the others in the local area, and see what it's really like.
In secondary schools, more classes are being taught by teachers without a relevant post-A-level qualification in the subject, it added.
Across all secondary subjects, 14 out of 17 had unfilled training places this year, compared with just two subjects five years ago.
Government policy to broaden the range of training routes has proved "confusing" for both training providers and applicants and could "discourage potential applicants," the report warned.
It added that the government spends £700m a year on recruiting and training new teachers but has missed its own targets by an increasing margin every year since 2012.
"Until the department meets its targets and can show how its approach is improving trainee recruitment, quality and retention, we cannot conclude that the arrangements for training new teachers are value for money," said NAO head Amyas Morse.
National Union of Teachers general secretary Christine Blower called the figures "a sad indictment" of government education policy.
"Unless government radically tackles the pay, workload and excessive accountability that teachers currently suffer, this is a situation that will get increasingly worse," said Ms Blower.
Head teachers' unions said the report echoed their own research.
"The acute difficulties recruiting in maths, English, science and languages are now extending to most other areas of the curriculum," said Malcolm Trobe, interim general secretary of the Association of School and College Leaders.
National Association of Head Teachers general secretary Russell Hobby warned of "a significant difference between official statistics and the perceptions of those in schools.
"We'd welcome the opportunity to sit down formally with the DfE... but as yet, they're not willing to acknowledge the scale of the problem."
Labour's shadow education secretary Lucy Powell called the report "a further wake-up call for the Tory government who have been in denial and neglectful about teacher shortages".
A Department for Education spokeswoman said the report made clear "that despite rising pupil numbers and the challenge of a competitive jobs market, more people are entering the teaching profession than leaving it, there are more teachers overall and the number of teachers per pupil hasn't suffered".
"Indeed the biggest threat to teacher recruitment is that the teaching unions and others, use every opportunity to talk down teaching as a profession, continually painting a negative picture of England's schools.
"The reality on the ground couldn't be more different, with the quality of education in this country having been transformed by the most highly qualified teaching workforce in history, resulting in 1.4 million more pupils being taught in good and outstanding schools compared with five years ago.
"But we refuse to be complacent," said the spokeswoman, who said the government was "investing hundreds of millions in teacher recruitment".