Moreover, the party's new leader carries neither scars nor baggage from that fearful period when Labour seemed to many to have condemned itself to oblivion. He was not even in the House of Commons when the great battle for the soul of the party reached its most bitter stages in the late Seventies and early Eighties. Popular support for the breakaway Social Democratic Party had already peaked long before Mr Blair was elected MP for Sedgefield in 1983. Ideologically, as well as in terms of age, Labour's torch has indeed passed to a new generation.
But this is not only a defining moment for Labour. It is a redefining moment for the Liberal Democrats. As the unofficial LDP journal, the Reformer, comments this month, 'it (Mr Blair's election) most obviously buries the Liberal Democrat vision of replacing Labour'. Shrewdly, the publication warns that what it describes as Paddy Ashdown's attempt to create 'artificial philosophical differences (between the two parties) will do us nothing but harm'.
What may well be happening is that the rough-and-ready self-correcting mechanism that Britain's unreformed political system contains, is completing its work. For the best part of a decade, this country had an embryonic three-party system, thanks to Labour's divisions, its perceived extremism and unelectability.
It was the role of the Alliance, and later the Liberal Democrats, to provide a refuge for those who would not continue to vote Labour but could not bring themselves to support the Conservatives. The ominous message the Liberal Democrats were sending to Labour - evolve or face the threat of extinction - did much to encourage the latter to reform itself. If Labour's modernisers have indeed succeeded, then Mr Ashdown and his reshuffled colleagues may have to come to terms with the fact that the Liberal Democrats' historic task has been completed and that they are once again members of a marginal party - albeit a worthy one that could still hold the balance of power after the next general election.
Mr Blair's achievement so far is, then, impressive. He appeals to his party and he resonates positively with much of the electorate. In addition, according to an Opinion Leader Research poll for this paper (published on Tuesday), Mr Blair has a substantial lead over John Major and all other political figures among senior industrialists, civil servants, media figures and similar opinion formers.
This domination Mr Blair has achieved in part because of his mood music - he has an impressive and attractive personality and style - and in part because of the policy signals he has been sending out. It is admirable to hear a politican say that tax loopholes aiding the very rich should be plugged - not because the sums involved are large (they are not) - but because he finds the existence of such loopholes morally distasteful. It is refreshingly unorthodox for a leading Labour MP to argue that large expenditure on the welfare state is more likely to be a sign of a failed economy than of an active collective social conscience. And it is radical (at least in this country) to suggest that unelected hereditary peers should lose their right to vote in the Upper House.
But all this does not add up to a coherent programme, or even a Big Idea. This autumn, Mr Blair intends to deliver a series of speeches outlining his policies, much as Harold Wilson did in the months before the general election of 1964 - which Labour won after spending 13 years in the wilderness. A great deal will depend on the success of this enterprise.
Many older voters still remember (albeit with a sense of incredulity) the excitement which the young Mr Wilson generated as he barnstormed his way across the country, projecting his party as a modern, managerial organisation, dedicated to bringing the white heat of technology to Britain's backward industries. It was the last occasion on which Labour seized the intellectual and ethical initiative and broke out of its historic ghetto to appeal to the young, the educated and the ambitious, to Middle England as well as to blue-collar workers.
If Mr Blair is to translate today's success into a Labour victory at the next general election - and the election of John Prescott as his deputy must further enhance the party's prospects - he will have to campaign as hard and as convincingly as Harold Wilson did three decades ago. He, too, must find a programme that appeals to the ambitious, the idealistic, and to those driven by a visceral distaste for the current tired and sleaze-stained political agenda.
And then, of course - as Prime Minister Wilson discovered in Downing Street - the going will begin to get really tough for Labour's new leader.