Divisions between Tony Blair and Gordon Brown have been almost incorporated into the British constitution. If there is an argument between the two men as to the size of the reduction in Britain’s EU rebate, then it would not be the first of its kind. Open disagreement between Mr Blair and John Prescott, on the other hand, is unusual. It is potentially more destabilising than the disharmony between No. 10 and the Chancellor. And so the Deputy Prime Minister’s public scepticism about the White Paper on education is a major and unwelcome development.

Mr Prescott could hardly have been less enthusiastic about reform while remaining in government. He muses that the city academy programme and the additional freedom which ministers want to offer to “trust schools” risks the return of the 11-plus. Such comments legitimise the charge that Mr Blair’s critics have issued against this blueprint. The Deputy Prime Minister is not a fool but he is clumsy. These do not, though, look like remarks that slipped out accidentally.

Mr Prescott’s concerns are a mixture of personal sincerity and political strategy. His dislike for academic selection made at a relatively young age is well-established and is based on more than bitter personal experience. But it is the prospect of a major Bill passing through the House of Commons only because the Conservative Party deigns to back it, while scores of Labour MPs reject it, that he regards with horror.

Mr Prescott spoke warmly in his interview of looking forward to a new “class war” with the “Eton mafia”. A war with David Cameron on the side of Mr Blair on schools against much of the Labour Party is not what he has in mind (always assuming that the promiscuous Tory leader does not change his mind and throw in his lot with the left wing of the Liberal Democrats and the Green Party on this policy).

The most depressing aspect of this stance, and not only from Mr Blair’s perspective, is how Mr Prescott misrepresents education policy. City academies have been founded and will continue to be created in areas of notable economic deprivation. The idea that they could become a meal ticket for the middle class is fanciful. The autonomy and independence envisaged for trust schools is that which church schools in the state sector have today and these are not normally accused of being de facto grammar schools. An official Admissions Code will limit the extent to which schools select pupils.

If Mr Blair cannot convince his own deputy that his plans would drive up standards for all and for the poorest in particular, then the hours that he is spending explaining his scheme to the lowly backbenchers are not likely to be fruitful. The quest to enact serious, substantial reform based on the votes of Labour MPs alone may be doomed.

There is, though, an alternative. Mr Prescott may recoil as the prospect of Mr Cameron providing the support required for this measure to reach the statute book, but that is the possibility with which he has to be confronted. If it takes an “Eton mafia” to empower the parents of children from the least wealthy backgrounds, then so be it.