The company confirmed that Chris Woodhead had resigned, barely two months into his new job as an adviser on regulatory policy, saying he was too busy.
It is also understood, however, that the former chief inspector had not been completely happy working outside education. The firm, chaired by Margaret Thatcher's former PR adviser Lord Bell, said it had not wanted him to leave, but accepted the decision, made in April.
Mr Woodhead's work for the Daily Telegraph, where he has contributed columns and articles since leaving the Office for Standards in Education in March, is now his main contribution to publicdebate.
The Tories were expected to make hay with his attacks on Labour, but neither education nor Mr Woodhead featured strongly in the party's election campaign.
It has been rumoured the Telegraph may not be entirely happy with the value they have got for Mr Woodhead's rumoured pound;100,000-a-year salary, a charge editor Charles Moore, strongly denies. Mr Moore said Mr Woodhead's recent low profile was explained by the enormous amount of work he had had to do on the paper's recent schools guide.
He added: "The Tories (in the campaign) have failed to capitalise on his arguments... They have not engaged much with education."
Ted Wragg, TES columnist and one of Mr Woodhead's fiercest critics, said:
"They should give knighthoods to the heads of Bell Pottinger and the Telegraph for getting Chris Woodhead out of OFSTED. The value of that act of service to education has been monumental."