When Blair has gone (for go he must), will Blairism follow him?

Is there - could there be - Blairism without Blair? That was the question that required a trip to Hungary last week. By the shores of Lake Balaton, an inland holiday resort, 11 "progressive" world leaders held a summit to discuss the future of centre-left politics.

Back at home, Tony Blair is on the verge of achieving something unusual - a third election victory. Yet he is persistently depicted as a rootless aberration, someone with no understanding of the history of his own party or the international tradition in which it lies. He stands accused of having little to show for his seven-and-a-half years in power. Again and again it is alleged that he has failed to entrench a progressive consensus that would reshape British politics.

In particular he is compared unflatteringly with the only other British prime minister to win three full terms on a full franchise, Margaret Thatcher, who, it is said, reshaped British attitudes and permanently shifted the centre of British politics to the right. The implication is that the purpose of winning elections is to change public opinion to make it safe for the Labour Party at last to get back to its proper business of redistribution at home and anti-Americanism abroad.

I would argue that there is a danger that the Labour Party might slip into such views like a comfortable old coat, which would help to ensure that it returned to being the natural party of opposition. To this extent I would agree with Blair's critics: that he has started a revolution, but that its success is still precarious.

The fragility of Blairism was well illustrated in Hungary last week. Even the name of the summit revealed the lack of clarity about how much the 11 leaders have in common. These gatherings used to be held under the banner of the Third Way, a deliberately ambiguous phrase adopted by Blair in the bliss of 1997's new dawn to suggest that New Labour was part of a worldwide phenomenon. But it did not catch on and, after Bill Clinton's presidency, it was replaced by the almost equally anodyne "progressive", while the membership of the informal club expanded across Europe and beyond. Last week's summit was attended by leaders of five European nations as well as those of Chile, Canada, Ethiopia, South Africa, New Zealand and South Korea.

Anodyne though it might be, at least "progressive" serves a purpose, in that it is avoids the use of words such as "left" or "socialist". That at least underlines the one simple insight on which the leaders do agree, namely that democratic politics is won in the centre.

As usual, though, Blair sounded the most right-wing of those attending. This was emphasised by the absence of the Americans, engaged in their presidential election campaign, and by the divisiveness of the Iraq issue. If the Americans had come to Hungary, they might have lent Blair support on issues such as crime and labour market flexibility, but John Kerry's anti-war stance would have added to the complications of Blair's photocall with leaders most of whom opposed the Iraq invasion.

What that means is that Blair is more aggressive in his defence of the centre ground, and possibly more aggressive than, say, continental European leaders need to be, given their countries' stronger social-democratic traditions.

But Blair is not an alien who landed in Britain from Planet Novelty 10 years ago. One of the rising stars of the New Labour constellation has just published a book called New Labour's Old Roots. Patrick Diamond, a Downing Street adviser who has just started working for Alan Milburn in his new cabinet job, tries to show in this collection that Blairism is the latest form of the long tradition of revisionist social democracy in Britain. It is a tradition that goes back at least as far as RH Tawney in the 1930s, defined by its willingness to revise the policies used to achieve the consistent objective of greater equality. Diamond reminds us that Hugh Gaitskell, the arch-revisionist, once thought it was a good idea to nationalise the machine tools industry. Times change; so should methods.

That much is (over) familiar to students of Blairite rhetoric. But New Labour is different from the rest of the tradition in two respects. One is that it does not use the language of equality much. The other is that it has been outstandingly successful electorally. An obvious question to ask is: are the two by any chance related?

I think they are. One of Blair's great skills has been his understanding of how language constructs reality in politics - in that respect, he is the politician most influenced by Jacques Derrida, who died this month. Blair recognises that equality is not the kind of word used by most people, even if they share the values of the progressive majority. Far better to focus on the weaker-sounding equality of opportunity, because genuinely giving everyone equal chances in life has radical implications that would in time make Britain a much more equal society.

More precisely, Blair understands that perception is reality. Recent polls have shown that, while the Labour Party is seen as moderately left-wing, Blair himself is seen as being plumb in the centre, or even a little to the right. The Conservatives, meanwhile, are seen as far out to the right and Michael Howard even further still. And guess where most voters place themselves? In the middle.

In other words, Blair is where he should be. But it is difficult to stay there, and any successor would be perceived as further to the left, not least because, in order to succeed him, he or she would need to win a leadership election among MPs, party members and trade unionists, whose sympathies lie well to the left.

There lies the big question for the future of the Blair revolution: How much has he changed the party? True, the party conference has been transformed. In a historical reversal, it is now the constituency party delegates who consistently rescue the leadership from defeats by trade union block votes. But one of the weakest passages in Blair's speech in Budapest before last week's summit was his assertion of the importance of building a "strong local party base". For a leader who inherited a party membership of 260,000, took it up to 405,000 and has now pushed it down below 200,000, this showed some chutzpah.

For the moment, it hardly matters, because Gordon Brown is the clear favourite to succeed. Whether or not New Labour is safe in his hands depends on whether he meant what he said last year about public services having to be publicly provided as well as publicly funded. But in two or three years' time, when Blair seems most likely to go, other candidates could emerge, and in the long run the durability of New Labour depends on the strength and depth of support for rigorous revisionism. Blair has certainly changed the Labour Party, but it is a weak and wasting base. I fear for the future.