Mr Blair's decision to preface the visit with interviews setting out his thinking on that relationship - and suggesting arbitration as a possible means of hastening a settlement in the long-running rail dispute - was prompted by two critical factors.
He has believed for some time both in the need for a speedy rail settlement and in the virtues of arbitration - provided for in the collective bargaining machinery of the industry. But Frank Dobson, Labour's transport spokesman, vainly tried to persuade Jimmy Knapp, the RMT leader, to call for it last week.
Second, he was provoked by John Edmonds's insistence in a newspaper article yesterday, in terms Mr Edmonds surely knew cut across the Labour leader's views, that the union relationship with the party was one of the 'defining links' in British politics.
Discreet attempts were made from within the TUC's ranks to stop Mr Blair meeting this challenge by saying in public what he believed in private. But he did not take long to ignore them.
Mr Blair was always bound, before long, to risk the anger of traditionalist union leaders, whose members gave him such a resounding mandate in the Labour leadership election. The moment came sooner than anyone, least of all his hosts in Blackpool last night, expected.
In his interview on BBC Radio 4's World At One yesterday, Mr Blair said: 'It is essential that we do not let this dispute drag on with all its inconvenience to the public when it could be settled by negotiation. It's not for me to say what the parties to the dispute should do. It's got to be negotiated free of political interference. I am merely pointing out that there is the facility of arbitration . . .
'Any sensible person, any sensible member of the public, would want to see a sensible solution to the dispute, which is a just one, bringing it to an end so we can get the railways back to normal.
'Of course I can see the justice of their case. This dispute has got to be negotiated between management and the unions . . . free from external political interference.'
On Labour's broader relationship with the unions, he said: 'Labour has to govern in the interests of the country as a whole. (The unions) are not asking for special privileges and access. They are asking for fairness. In my view, the vast majority of trade unionists accept and understand that.'
At a dinner yesterday evening Mr Blair told members of the TUC's general council that there were some issues on which a future Labour government could not deliver, writes Barrie Clement. He did not elaborate, but some of the left-wingers present believed that the comments presaged early disappointments if the party won the general election.
In a jocular after-dinner speech he said, however, that Labour would introduce a national minimum wage, a new Bill of employment rights and would attempt to secure full employment. He counselled union leaders against complacency and warned them that the Tories would have no scruples during the election campaign.