A critical shortage of teachers means children will be taught fewer subjects in larger classes by less qualified people, a government adviser has warned, as new figures reveal that ministers are dismally failing to meet their recruitment targets just days ahead of the new academic year.

Across a range of key subjects, the number of trainee teachers recruited for 2015 is significantly below the target figures, with some disciplines attracting barely half the numbers that were being sought.

The figures – quietly published last week – suggest there will be a 10% shortfall in trainees starting next month. It will be the third year in a row that the government has failed to hit the targets contained in its teacher supply model.

The figures show there is a 57% recruitment shortfall in trainee design and technology teachers and a 37% shortfall in religious education teachers. For music teachers the shortfall is 25%, the same as for geography, while for teachers in the key subjects of English and maths the shortfall is 12% and 11% respectively.

Writing in the Observer, Prof John Howson, who advised on this year’s teacher supply model, said: “Without drastic action, more headteachers will be forced to employ staff not qualified in their subjects or for the age group they are teaching, or simply remove subjects from the curriculum.

“Parents may find they need to rely more on private tutors when schools cannot guarantee the grades that pupils will achieve. The government has acknowledged that it faces a challenge, but not a crisis. Unless it recognises the scale of the problem and acts soon, it will become the worst teacher-supply situation since the dark days of the early 2000s. That is no way to create a world-class education system.”

The numbers recruited overall who will be qualified in time to start teaching in the 2016 academic year are marginally higher than last year, but appear to be inflated by a huge influx of language teachers, where supply far outstrips the government’s target.

Howson, who was the government’s chief adviser on teacher supply in the mid-1990s, said he believed those numbers could be explained by a recent surge in immigration. Net migration to the UK is at an all-time high, reaching 330,000 in the year to March, the Office for National Statistics revealed last week.

Chris Waterman, chair of the supply and teacher training advisory group, said a “perfect storm” of factors had led to the crisis, including attacks on the profession by ministers and Ofsted, a rise in pupil numbers, the decision to stop paying off teachers’ tuition fees, and an improvement in the country’s economy, which had led possible applicants to look elsewhere for work.

He warned that real-term cuts in teacher pay, as well as George Osborne’s recent pledge to keep public sector pay rises to 1% for the next four years from 2016-17, had also discouraged applicants.

He said: “The rise in pupil numbers, which is easy to predict from birthrates, is putting huge pressure on school places and an increasing demand on the shrinking pool of teachers. More and more teachers are moving abroad to teach, often with much lower income tax and much better benefits. Many headteachers are losing sleep or having nightmares about how to find appropriately qualified teachers to teach their students.

“Inevitably, it’s the schools in challenging circumstances that are at the end of the queue for teachers.”

Schools minister Nick Gibb said the number and quality of teachers was at an all-time high but the government recognised the difficulties in recruiting people into the profession in recent years.

He said: “These figures show that teacher recruitment is improving, with 3% more people due to start postgraduate teacher training than this time last year. We have already exceeded our target for primary school trainees and are making sustained progress for the secondary sector – including in key subjects like English, maths, physics and chemistry, where we are ahead of last year’s performance.

“We recognise, however, that recruitment is a challenge as the economy continues to strengthen and competition for new graduates intensifies, which is why we are focused on attracting more top graduates into the profession, particularly in those core academic subjects that help children reach their potential.”