Michael Dopson, acting head of Oriel high school, near Great Yarmouth, wrote to parents only two weeks ago warning that all but Year 11 pupils would have to spend one day a week studying at home unless the school could fill six teaching vacancies over the summer.

A spokeswoman for Norfolk County Council confirmed the position. She said:

“The head was talking about some of our pupils being taught 80 per cent of the curriculum in school, and 20 per cent in the home. That has not changed, as far as we are aware.”

Surrey, which has 200 vacancies, and West Sussex, with 60, were also unsure whether schools could avoid reduced timetables.

School standards minister Stephen Timms was accused of “complacency” after claiming in a radio interview this week that most teacher vacancies would be filled in time for the new academic year.

Mr Timms said: “The indications are that we should have, I think, the teachers that we need by September, but there is a good deal of work to be done between now and then.”

Later, at the Professional Association of Teachers conference in Cardiff, Mr Timms said that every council his officials had spoken to had said it did not expect a reduced timetable.

But a Tory survey of 121 secondary schools showed no sign of a turnaround over shortages, with one head in two reporting at least one unfilled vacancy and one in 20 with five or more posts to fill. Shadow education secretary Theresa May accused Mr Timms of “extreme complacency”. Recruitment expert John Howson said: “The minister is like an ostrich sticking his head in the sand.” Jean Gemmell, PAT general secretary, said:

“I wish I could share Mr Timms’s optimism.”

Mr Timms had been responding to TES editor Bob Doe’s prediction on BBC Radio 4‘s Today programme that the staff shortage this year will be at least as bad as last year, when a joint survey with the Secondary Heads Association suggested there were 4,000 vacancies in secondaries alone.

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