Blair's "speech" to the trade union leadership during TUC conference - the written version of it circulated to the press - laid it hard on the line. That Blair's administration should act like a left-wing government is, he told them, simply ruled out. Return to a Labour Party seriously influenced by the unions was, he insisted, fantasy.
"The idea of a left wing Labour Government as the alternative to a moderate and progressive one is the abiding delusion of 100 years of our party. We aren't going to fall for it again".
By "moderate and progressive" he means the sort of profit-serving government that keeps anti-union laws on the statute books, privatises, and does all the rest of what New Labour has done in office, having stolen the Tories' political clothes and left them shivering on the fringes of serious bourgeois politics.
When Blair said that the idea of a left-wing government was "the abiding delusion of our party", it was not quite true. Some Labour Governments have been broadly left-wing, and not only in comparison with the present neo-Thatcherite New Labour Party.
The 1945-51 Labour Government created the welfare state, introducing the sort of reforms which Karl Marx, referring to a law to limit the working day of children to ten hours as his example, called "the political economy of the working class".
Yet Blair's words also had an important part of truth. The Tories have been the "natural party" of bourgeois government. Labour governments have come to power and tried to balance between running capitalism as it needs to be run, according to its own laws, and throwing some sops to their working-class supporters.
They have frequently faltered on the contradictions between those two functions. The Labour Party has often been in open antagonism to Labour governments.
By the end of the Wilson-Callaghan government of 1974-9, the Labour Party was virtually at war with the Government. So much so that the left - on the initiative of Socialist Organiser, Solidarity's predecessor - was able to run a number of Labour candidates in the 1979 election on a platform of open hostility to the outgoing Callaghan government.
When Thatcher defeated Callaghan in June 1979, the Labour Party exploded. "Never again" became the dominant cry in the Labour Party.
Eighty-three per cent of the Constituency Labour Parties voted for the left-wing standard-bearer Tony Benn for Deputy Leader, and they put in long-time "soft left" Michael Foot as party leader.
And then the tide of mass unemployment, on a scale unprecedented since the mid-1930s, the damping-down of working-class militancy which it led to, and the growing hegemony of Thatcherism in the country, especially after the 1982 Falklands war, knocked the heart out of the Labour left.
The long slow crawl into the political camp of neo-Thatcherism began under renegade leftist Neil Kinnock. The new dominant coalition of the Labour Right and soft left privately adapted the left-wing cry of 1979, "never again" and gave it a new meaning. What they meant was that "never again" should the Labour Party create expectations in its supporters that would lead them to cry "betrayal" at a government like Callaghan's or Wilson's.
Neil Kinnock is quoted as saying, cynically: "We'll do our betraying before we take office".
He prepared the way for the Blairite coup of the mid 90s, which produced a New Labour Party whose leader was not ashamed publicly to assure the Tory Daily Mail that he would, if elected, keep the Tories' "most restrictive labour laws in Western Europe" on the statute book.
He produced an outspokenly bourgeois government. The then leaders of the unions backed him to the hilt. One of them, Alan Johnson of the CWU, became an MP and is now an identikit overdressed lacklustre minister.