Stephen Byers, 43, is the man with the legal brain. He is also, as one union source put it in Blackpoool, an "arch-moderniser" who is close to the Labour leader. But he is new to the employment job. He was brought in during the summer, against the backdrop of tube, rail and postal strikes, to tighten policy on industrial relations, particularly on public-sector strikes. One MP suggested that, when Mr Byers speculated so indiscreetly over dinner with journalists last week about the future of the Labour- union link, he was failing to appreciate his own importance in the party hierarchy. "He needs to understand," the MP said, "that, when he says something, even in private, journalists are going to give it a great deal of attention."
Nevertheless, it says much about Mr Byers's reputation that Tony Blair did not hesitate to back him. Less media-friendly MPs would have gone to ground; Mr Byers was trusted to take his case to every conceivable news programme on Friday.
Ian McCartney is the man with the working-class and union background; he served as a campaign manager for John Prescott. He joined a union and the Labour Party at 15 and, in his Who's Who entry, describes himself as "head of the McCartney family, a family of proud working-class stock". He is in charge of minimum-wage plans and that, according to one union source, "reassures us that Labour is really committed to the plan".
But the most intriguing presence on the team is that of Peter Hain, an exiled South African who fought passionately against apartheid from the 1960s. He has a formidable knowledge of the unions, after nearly 15 years as research officer for the Union of Communication Workers. He joined Labour in 1977.
Mr Hain's hallmarks are meticulous preparation and hard work. His brief is to make an issue of job insecurity.
His contacts are excellent. As one union official put it last week, "at Blackpool it takes him an hour to walk from one end of the Winter Gardens to the other because everyone wants to stop and chat to him".
But can he be entirely comfortable in a team whose leader, David Blunkett, said last week that the party would "not tolerate the activities of armchair revolutionaries whose only interest is disruption"?
In 1986, Mr Hain published a book called Political Strikes, in which he was highly critical of traditional trade unionism. But his proposals for "modernisation" were not exactly of the sort that Mr Blair has in mind. The essence of his argument - supported with frequent references to "struggle" - was not that unions should hesitate to use their muscle, but that they should use it for wider ends than better pay and shorter hours. Further, he envisaged a Labour government backing them. "New trade unionism will involve collective bargaining ... It will also include positive strikes where they are required to gain increased control. Such strikes - for example against an obdurate private employer who resists disclosure of information or proposals for industrial democracy - will need the support of Labour ministers, so that the authority of government is harnessed with shopflooor power."
Hardly new Labour; rather, very old syndicalism. Mr Hain was particularly severe on the then Labour leadership's failure to support the 1984-5 miners' strike. "Fastidiousness" about picketing, he argued, failed to take account of "the seriousness of the class battle being waged". Since workers only had strength in numbers, they were understandably hostile towards their fellows who threatened it. "They are therefore justified in so organising picket lines that they can only be crossed by very determined individuals ... Furthermore, if it is to have any effect upon those at whom it is directed, a picket must serve as a reminder of the workforce that it represents, and a mass picket is the authentic reflection of a large workforce."
But consistency has never been Mr Hain's strong point. Or, as friends put it, he adapts to changing circumstances. One said: "In the old days he had to be prevailed upon to drink the occasional glass of wine. Since becoming MP for Neath, he's learned how to sink pints and sing rugby songs."