Comprehensive education is, after all, one of Labour's tribal totems, second only to the National Health Service. That is why the threat that trust schools allegedly pose to it provokes Lord Kinnock, the greatest of the tribal elders, into the only significant public criticism he has ever made of Mr Blair and new Labour.
True, most comprehensives came into being under Margaret Thatcher's reign at the education department in the early 1970s. But ownership, as the management gurus would call it, was undeniably Labour's.
Such was the momentum generated by Anthony Crosland, Labour's education secretary from 1965 to 1967, that it was impossible for Mrs Thatcher to reverse the policy, though she did her best to sabotage it by making absurd rulings that some grammar schools must remain open in order to preserve "choice".
Very few other traces remain of pre-Blair Labour achievements. Industries have been de-nationalised, social security turned upside down, pensions allowed to dwindle, and employment law tilted in favour of the boss class.
The social reforms of the 1960s - legalisation of homosexuality and so on - remain, but they were liberal rather than socialist ideas and many went through the Commons on free votes. Take away the NHS and the comprehensives, and you might as well write off the first century of Labour party history.
I would not, therefore, underestimate the importance of the Education Bill when it is finally published next month. The party has tolerated Mr Blair on the understanding that its tribal totems, which another term of Tory government after 1997 might have up-ended, were sacrosanct.
Why is Mr Blair so stubborn on this subject? He can certainly get away with his "trust schools" if he allows back local authority control of admissions. Why is he so reluctant to make this concession?
The answer is that there is no point in trust schools unless they are allowed to operate as he envisages. Even Mr Blair surely understands that schools now have as much independence of local authorities as they can possibly wish for.
People talk of the local authorities' dead hand, but I have never heard anybody explain what it is that schools might wish to do if it were removed. All the restrictions on teaching and learning come from the centre. As for diversity and enterprising experiment, local authorities provided infinitely more than exists now.
I am old enough to remember when a Highbury Grove, run on traditional lines by the very right-wing Rhodes Boyson, and a William Tyndale, excoriated as the most outrageous example of trendy teaching, could exist within a few miles of each other in the London borough of Islington. Schools can now do little more than fiddle around with the opening hours.
No, the trust schools must have control of admissions if they are to satisfy the two constituencies to which Mr Blair has chosen to ally the Labour party. The first is business. Labour has struggled to get business sponsorship for schools, even when the sums required have been small.
Business won't put up money unless it has complete control, including control of admissions, and it certainly doesn't want to tangle with local authority committees.
The second is middle-class parents. They don't much care whether a school is academically selective or not - on the whole, they'd rather not because it might select out their own children - but they want it to have the power to keep out the yob element. As a parent who himself had to choose comprehensives for his children, Mr Blair has a better insight into this than any previous prime minister.
The Labour party has accepted alliances with business and the middle classes as it has accepted the rest of Mr Blair's antics. One provides money, the other provides votes. The party will not easily accept the death of comprehensives - and it believes that, once schools have complete control of admissions along with powers to expand, we shall be half-way back to grammar schools.
I make no bold predictions, except of an outbreak of backbench handwringing. Mr Blair may fall, or he may not. He will certainly not do a Ramsay MacDonald and go over to the Tories. But I do wonder if he will still be a Labour party member in 10 years' time.