Our survey paints a picture of a party in transition, with new Labour councillors leading a "New Labour" revolution.
On the morning after the local elections, Mr Blair seemed to share the expectations of the Conservatives that many of his new councillors might indeed be "old Labour" militants, when he reminded them of their "special responsibility" as "ambassadors for New Labour".
But his fears seem misplaced. In the councils we surveyed, gesture politics is dead and high spending has been stopped by capping laws. Some "old Labour" beliefs still have a strong emotional pull, but are being sublimated in a changed world. "Pragmatism", "realism" and "serving local people" are the new recurring themes.
There are two kinds of new Labour councillor. About half are long-standing party activists, who have often been councillors in the past, or are jumping ship from county councils which are about to be abolished. The "genuinely new" councillors tend to be in their thirties, usually men despite all Labour's attempts to increase the proportion of women, and to agree with Mr Blair that the party has to change, although some of the changes they find hard to take in practice.
The evidence of our survey is that the younger, more recent party members tend to be more "New Labour" than their experienced colleagues. But many of the old guard have undergone a change of heart, and a union tie does not necessarily mean "old Labour".
Moss Evans, the former general secretary of the Transport and General Workers' Union, is a remarkable symbol of Labour's change. He has been reincarnated as the Labour leader of King's Lynn council, aged 70. He does not sound like the union boss who brought down James Callaghan's pay restraint policy in 1978: "Our priority is good relations with the business community to generate new employment. We are not going to create any sort of revolution, our approach is pragmatic. We cannot increase spending really, but we do have different values and different priorities."
Relations between Labour councils and their employees are now as distant in nature as they are in time from the winter of discontent 16 years ago.
Portsmouth, where Labour took control of a "hung" council on 4 May, is an extreme but not unimportant example. Last year the minority Labour administration began an aggressive programme of putting services out to commercial tender. The press office is supposed to call it "externalisation", but Leo Madden, the leader, is happy to call it privatisation. Earlier this year, leisure, refuse collection, building and grounds maintenance services worth £18m a year were hived off. And on 4 May Labour gained four seats from the Tories to win a majority of one.
The defence-dominated city, which sent off the Falklands task force in 1982 in a spasm of jingoism, is a symbolic gain for Labour as important as its advances in Essex. Many Labour councillors work in defence-related jobs, and the Conservatives ran the council from its creation in 1973 until the poll tax elections of 1990, when Labour took over in a joint administration with the Liberal Democrats.
Mr Madden, a "pragmatic rather than ideological" civil service union official, says privatisation "did cause us trouble with the local Labour Party, and still does", but he emphasised that 60 per cent of council staff had backed it. He boasts that he has "relentlessly pursued non- poll-tax-payers", allowing an 11 per cent cut in council tax.
Despite Conservative propaganda about average council tax levels, there is usually surprisingly little difference between the parties on spending. The Tory averages are lower because a minority of Tory councils spend considerably less than the Government allows them to.
But in most cases where Labour is taking over from the Tories, it finds that the council was already spending up to its cap limit. Tory laws have drawn the sting of one of the fiercest arguments between the parties.
Brian Wilson, a new councillor in Castle Point, when asked what Labour had promised in its local manifesto, said: "Not a great deal. We're realistic."
On the important question of what might happen under a Labour government, it was hard to detect huge pressures for greater spending. Jack Straw, as shadow Environment Secretary last year, made it clear that some form of capping would remain. And defiance of the law is no longer espoused anywhere.
Perhaps the most striking evidence of "Newness" is in the attitudes of new Labour councillors to Shadow Chancellor Gordon Brown's "New Economics" - including his refusal to pledge higher taxes on the better-off. This was an issue which caused widespread dismay among party members in 1993, when Mr Brown only just scraped on to the national executive committee in last place.
A new councillor in Portsmouth, Terence Bryant, a 36-year-old blue-collar government service worker in the TGWU, backed Mr Brown, although he said the tax system had to be made fairer: "We will get nowhere if we don't learn from past history. That is one of the things which killed us in 1992."
Graham Heaney, another new councillor in Portsmouth, said taxes on the better-off should not be raised "as a matter of principle - it is a purely pragmatic decision; if we have to do things for the education and health services, then we should say to people that they have to pay more".
Our survey suggests that the arguments of the "modernisers" have won more ground at this important level in the party than many realise - although the unexpectedly high 85 per cent vote among party members for the new Clause IV did demonstrate a dramatic change in grass-roots opinion. There are dangers in Labour's dominance of British local government - but they are not the dangers of the gap between Labour councils and public opinion which plagued the party in the Eighties. The danger is rather that incidents of incompetence or corruption will stand out in the overwhelmingly Labour landscape.