The Government has missed its teacher recruitment targets for the last four years despite spending £700 million annually on their training, according to the National Audit Office (NAO).
A report released by the spending watchdog also revealed that indicators suggest teacher shortages are growing.
Between 2011 and 2014, the recorded rate of vacancies and temporarily filled positions more than doubled from 0.5% of the teaching workforce to 1.2%.
The report states that the Department for Education (DfE) has a weak understanding of the extent of local teacher supply shortages and whether they are being locally resolved.
It highlights the problem in poorer areas, with some 54% of leaders in schools with large proportions of disadvantaged pupils saying attracting and keeping good teachers was a major problem, compared with 33% of leaders in other schools.
Amyas Morse, head of the NAO, said: "Training a sufficient number of new teachers of the right quality is key to the success of all the money spent on England's schools.
"The Department, however, has missed its recruitment targets for the last four years and there are signs that teacher shortages are growing.
"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."
Additionally, the NAO says that more secondary school classes are being taught by teachers without a relevant post-A level qualification in their subject.
In one example, the proportion of physics classes being taught by a teacher without such a qualification rose from 21% to 28% between 2010 and 2014, the report, called Training New Teachers, says.
It further shows that secondary school teacher training places are proving particularly difficult to fill, and that the DfE cannot recruit enough trainees in the majority of secondary subjects.
In the year 2015/16, 14 out of 17 secondary subjects had unfilled training places, compared with two subjects with unfilled places in 2010/11.
The report states that while the DfE and the National College for Teaching and Leadership have increased the number of routes by which people can qualify, potential applicants do not yet have good enough information to help them decide where to train.
Providers and schools told the NAO the plethora of training routes was confusing.
The NAO found that 53% of the 44,900 - full time equivalent - teachers who entered the profession in 2014 were newly-qualified, with the remainder either returning to teaching after a break or moving into the state-funded sector from elsewhere.
It said the Government needs to do more to demonstrate how new arrangements are improving the quality of teaching in classrooms.
Between 2011 and 2014 the number of teachers leaving the profession increased by 11%, and the proportion of those who chose to leave the profession ahead of retirement increased from 64% to 75%.
Shadow secretary of state for education Lucy Powell said: "This NAO report should be a further wake-up call for the Tory Government who have been in denial and neglectful about teacher shortages.
"The teacher recruitment and retention crisis is serious and growing, with schools struggling to get teachers with the right qualifications in front of classes in subjects vital to our country's economic success, such as maths, science, English and modern foreign languages."
Malcolm Trobe, Interim General Secretary of the Association of School and College Leaders, described the teacher shortages as "severe", adding that they were already "jeopardising standards".
He continued: "The situation is likely to worsen without urgent action. This is because the number of pupils is set to significantly increase over the next few years and many more teachers will be needed.
"Changes in the curriculum will make shortages even worse in high demand subjects."
A Department for Education spokesman said: "This report makes 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 haven't suffered."
The biggest threat to teacher recruitment is that the teaching unions and others use every opportunity to talk down teaching as a profession, the spokesman continued.
"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 and are determined to continue raising the status of the profession so that every child has a great teacher. That's why we're investing hundreds of millions in teacher recruitment, backing schemes like Teach First and the National Teaching Service to get great teachers where they are most needed, and why we've given schools unprecedented freedom over staff pay, to allow them to attract the brightest and the best."