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Teachers' union leaders are warning that teacher shortages are costing schools hundreds of millions of pounds in temporary supply staff.

The National Union of Teachers says schools in England spent £733m last year on supply teacher agencies.

The union says it is wasting money intended for children's education.

Education Secretary Nicky Morgan is launching a TV recruitment campaign to attract a "new generation of passionate and gifted teachers".

Head teachers have been reporting deepening problems with getting enough staff.

The Department for Education has launched a television advertising campaign to encourage more applications, saying that 35,000 trainee teachers need to be recruited every year.

There are particular problems in finding teachers in subjects such as physics, and the government is offering increasingly generous bursaries.

A physics graduate with a good degree can claim up to £30,000 tax free for entering teaching.

"Great teachers are at the heart of our drive to extend opportunity to every single child," says Mrs Morgan.

"That is why we are focused on attracting more talented people into the profession, to inspire young people, open doors to their future."

The teachers' union argues that the difficulty in recruiting teachers means schools are forced to use their budgets on supply staff - and that these temporary staff are not receiving the same pay and benefits as full-time teachers.

"Supply teacher agencies are making millions while supply teachers' pay continues to plummet," said NUT leader Christine Blower.

"This is money which should be used for children's education, not going towards boosting the profits of private companies."

The Recruitment and Employment Confederation rejected the NUT claims as unfair and said schools with vacancies "rely on their recruitment partners to bring in quality teachers, often at very short notice".

"Agencies charge a daily rate for temporary contracts and the majority of this will go directly to the teacher. It is up to schools, agencies and teachers to negotiate pay rates and this can vary according to location and other factors such as how much experience the teacher has," said head of policy Kate Shoesmith.

She said agencies "typically take between 15-30% cent of the fee".

Russell Hobby, leader of the National Association of Head Teachers, said: "Heads are increasingly forced to rely on supply agencies because they can't find permanent staff in time.

"This creates real problems with continuity and coherence, particularly important with vulnerable children. It is also expensive at a time of increasing budget pressures.

"If the recruitment pressures continue, more drastic measures are just around the corner, including appointing non-qualified staff, narrowing the curriculum or increasing class size."

Labour's shadow education secretary Lucy Powell said that school budgets are already under pressure, but "head teachers are turning to agencies in desperation to fill the gap".

"Ministers need to take real action to recruit and retain teachers in sufficient numbers to tackle the crisis in schools which is threatening standards."