What of the other contender, Iain Duncan Smith? Right-wingers mutter approvingly about his support for caning in schools, but rather more intriguing is his approval of the Dutch education system, where schools are voluntary, private and non-profit making.
Conservative after Conservative has lined up to say the party must get back to the basics of providing good public services, and downplay the row over Europe. Yet so unimportant has education been in the party's quest for a new leader that its only moment in the spotlight came over Section 28, the notorious bit of Thatcherite law that prevents local authorities "promoting" homosexuality in schools. Unfortunately, front-running candidate Michael Portillo made the mistake of honestly answering a question about the future of Section 28. Many think that finally buried his chances.
But as the Tories have talked the talk, Tony Blair and Estelle Morris have been walking the walk on actual reform of public services, but to a reception even chillier than they must have anticipated.
At the weekend came news that the publication of the much-heralded White Paper on education was being delayed from this week to September, officially because time had been too short to complete it after the election was put back a month. And, Ms Morris told David Frost helpfully, she wanted teachers to have the chance to join the debate when they were back in school in September.
Stories circulated, meanwhile, that the delay had more to do with a desire to cool the row with the unions after new minister Stephen Timms' pronouncements on privatisation. There was also talk of tensions between the Department for Education and Skills, the Treasury and Downing Street.
Tony Blair ran into his costly little local difficulties with the unions on much the same issue, leading to the giant GMB withholding pound;1m it had planned to donate to Labour over the next four years. It will use this cash instead for an anti-privatisation publicity campaign.
Estelle Morris - though much liked by civil servants and the press - has not had a good week, still apologising for the AS-levels fiasco and having to explain the White Paper delay.
The Daily Mail put the boot in, criticising decisions to relax rules on trainee teachers' literacy and numeracy tests and the "watering down" of maths targets for 14-year-olds, likely four-day weeks in September and other developments.
It opined: "Any previous Education Secretary just one month into the job could perhaps expect to be given the benefit of the doubt ... But Miss Morris spent the past four years in the Education Department rising to become Mr Blunkett's highly regarded deputy.
"Now she has risen to the top job, she knows she has to prove that she is up to the challenge. Her end-of-term report would almost certainly say 'must try harder in order to fulfil her potential'."