Mr Norris, former transport minister for London, said the Tories should be "ashamed" of their failure to significantly improve the level of education in state schools."
He accused the Tories of failing state schools on two counts, through a lack of resources, and through the refusal of Lady Thatcher, a former education secretary, to give state education sufficient priority.
"I think Mrs Thatcher took the view that state education was there for those who couldn't provide for themselves. State education was very much lower down her own agenda than perhaps it ought to have been," Mr Norris said.
His remarks went out on BBC 24-hour television at 4.05 am yesterday and he may have been hoping they were not noticed, but they were picked up by the eagle-eyed night shift of the Downing Street media monitoring unit and raised at Prime Minister's question time in the Commons.
Mr Norris is regarded as a potential Tory candidate to run for mayor of London, but has so far failed to throw his hat in the ring.
His remarks were seen as a possible bid for cross-party support from Labour for the contest against Lord Archer, who has already declared his interest in the job. "We are waiting now for Jeffrey Archer to come out attacking Lady Thatcher," said a Downing Street source.
But, as the Independent reported on Monday, there is growing cabinet backing for Glenda Jackson, Mr Norris's successor as transport minister, to gain Labour's endorsement as the candidate for the election of a mayor for the capital if a referendum on the post on 7 May produces a `yes' vote.