On the platform, television's favourite Labour politician was flanked by the actor who plays Chief Inspector Brownlow of The Bill, and a former host of That's Life. A thousand Southern voters, including many Labour activists, applauded as Mr Blair castigated the Tories' record and called for a one-nation Labour government. The only distraction was the sound of energetic play from the centre's squash courts.
Eastleigh, where on Thursday voters will take part in a by- election as well as the European elections, is the type of seat Labour needs to win if it is to form the next government. Adjoining Southampton Itchen, which is held by Labour's John Denham, it boasts an industrial base. Yet here, as in swaths of the South and South-west, it is the Liberal Democrats who are poised to win this week.
Can Mr Blair make the difference? Some Conservatives think he can. One former minister said last week: 'He seems to be growing into the part. He is not going to make too many mistakes; he understands TV and is completely clinical. It's a squeaky-clean routine, absolute Persil.' But the public seems to approve. As he waited for the London train, Mr Blair's takeaway Big Mac grew cold as he dealt with the greetings of fellow passengers. It was a rather different meal from the one over which he was all but handed the Labour leadership, in the fashionable Granita restaurant in north London.
This was the moment that the shadow Chancellor told Mr Blair of his decision not to run. But it seems that Mr Brown had made his mind up earlier, probably a week ago. Eighteen months before, the assumption was that if a contest took place, Mr Blair would stand down for Mr Brown. But things had changed. The opinion polls consistently put Mr Blair well ahead. Mr Brown's backers believe he had as many supporters in the parliamentary party and the unions as Mr Blair. But it is unlikely that all would have stayed loyal.
Anxious to avoid a bruising contest, the shadow Chancellor also believed that even if he proved victorious, he would have been labelled by the media as the man who stopped Labour's best hope. The Granita meeting was fixed with Mr Brown prepared to stand aside, providing certain conditions - chiefly his continuing as shadow Chancellor - were met.
On Wednesday morning, Mr Brown and shadow Cabinet colleagues, including the acting leader, Margaret Beckett, agreed that it was inevitable that news of the Brown campaign being ended would leak out, and so an announcement was made.
The reaction on the left and in some of the trade unions was hostile. But because of last year's reforms, the unions' role is limited to the influence they can exercise over the votes of their members, and many union executives are reluctant to back any of the candidates publicly. As one Labour official put it: 'The unions appointed John Smith. This time John Edmunds is going around putting a list of questions to potential candidates and Bill Morris is organising a debate. The difference is stark.'
Mr Blair expects a leadership contest and realises that to inherit the top job without one would weaken, rather than strengthen, his mandate. He is, however, careful to make clear that a Blair leadership would not signal a new phase of modernisation of union links. The Labour Party he is set to inherit is pretty near the one he wants to lead, although it needs a greater sense of identity.
Of the three serious contenders, the one whose candidature looks most certain is John Prescott, the employment spokesman. Relations between Mr Blair and Mr Prescott have been good and should withstand a leadership battle in which Mr Blair proved victorious. There is, Mr Blair's friends say, no danger of Mr Prescott suffering the same fate as Bryan Gould after his abortive challenges for the leadership and deputy leadership nearly two years ago.
Robin Cook, the trade and industry spokesman, is still undecided about standing. That leaves Mrs Beckett, whose friends are convinced that she will run. Ironically the Granita dinner may have strengthened the resolution of her backers who were angered at reports - quickly and hotly denied by the Blair camp - that Mr Brown had been promised overall control of Labour's social and economic policy. 'It sounded a bit like an old-fashioned stitch- up,' said one left-winger.
Mrs Beckett's supporters believe she could assemble a powerful coalition of backers. But the Blair camp is in optimistic mood. And on Thursday, John Denham reminded the Eastleigh audience of the shadow Home Secretary's hunger for office in a Labour government. Mr Blair greeted Mr Denham on his arrival as a new MP at Westminster after the 1992 election. As they stood outside the Houses of Parliament, a ministerial car swept by. 'I'll swear,' Mr Denham said, 'that his eyes misted over.'
Tony Blair now stands at 8-1 on to win the forthcoming Labour Party leadership race, according to William Hill, the bookmakers. John Prescott is 9- 2, with Margaret Beckett, the current leader at 20-1.
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