Teaching Personnel, the firm which launched a pound;50,000 prize draw to lure recruits, is considering offering teachers working in areas with acute shortages the chance to receive a jab worth pound;60.

Graham Hellier, the company’s chairman, said the agency is already struggling to find supply cover in several areas. With demand set to double in January and February, traditionally the worst months for teacher illnesses, all supply agencies face the problem of letting down hundreds of schools, he said.

Mr Hellier added: “We have not decided yet whether we will make this offer, or whether we would pay the full, or half the cost of the jab.

“If a teacher did not have the jab, and we end up having a day when we cannot supply to a school, the loss would easily outweigh the cost of having them vaccinated forthat period.”

Teaching Personnel has 6,000 teachers on its books, but the offer would only be made to those on its guaranteed payment scheme, which pays teachers even when the company cannot find them work for the day.

Mr Hellier said the Government should be considering free flu jabs for all teachers, claiming it could save schools money and save pupils being sent home.

Sheffield’s recruitment companies ran out of supply teachers on one day this month. The head of one of the city’s largest comprehensives had been forced to put pupils in classes of 45 as a result.

Steve Petherbridge, managing director of the agency Supply Desk , said: “This is meant to be a quiet time. But already we are busier than we were in July. It’s crazy.”

Last month, a TES survey showed that there were up to 4,000 teacher vacancies in England and Wales at the start of term. Already,pupils in two schools have been put on four-day weeks because of shortages.