The party says the metaphor is flawed, because the "teenager" has increasingly tapped into other sources of funding. According to the national executive committee's latest financial statement, unions contributed pounds 3.5m in affiliation fees to the party treasure chest in 1985, 80 per cent of the income. Then, unions also commanded 90 per cent of the vote at the policy-making annual conferences.
In 1994 affiliates contributed 57 per cent of Labour's pounds 11.7m income, the report says. Party officials now estimate it as nearer 50 per cent at a time when unions' voting power has also been cut to half.
But the figures do not give a complete picture: 70 per cent of the last general-election "war chest", for instance, came from union affiliates. And while the party spends nothing on gathering unions' affiliation fees, there is a considerable cost attached to fund-raising activities. Part of the "non-union" contributions elicited by the party rely on the good offices of unions. The commercial unit receives an income by organising union conferences and exhibitions for most of the party's largest affiliates. As one union official pointed out: "If it wasn't for us, the fund-raising figures would not look half so good."
Unions also sponsor constituencies and regional Labour organisations, not forgetting cash vouchsafed to the front bench for research. Then there is the party's Walworth Road headquarters, which is owned by unions and rented to Labour at a "non-commercial rate". The Office of the Leader of the Opposition has expanded unprecedentedly under Mr Blair, with 20 staff listed in the most recent Commons directory.
Mr Blair began his leadership with a pounds 9,000 surplus from the pounds 88,000 raised by his leadership election campaign team and has continued to attract funding, both from trade unions and - to a record extent - from businesses as it has seemed more and more likely that he will become prime minister.
He inherited from his predecessor, John Smith, an arrangement by which donations for his private office were channelled through the Industrial Reform Trust. The secretive trust was run by Lord Haskel, a friend of Smith and former associate of Lord Kagan, Harold Wilson's business ally.
Earlier this year Mr Blair distanced himself from this reminder of the past and set up a "blind trust", the Labour Leader's Office Fund, to receive donations. Only the trustees, Lord Rees, Baroness Jay and Baroness Dean, know the identity of donors. No one in Mr Blair's office knows who the donors are and therefore cannot be influenced by that knowledge, said a spokeswoman.
But it is well known that David Sainsbury, chairman of Sainsbury's and former bankroller of the SDP, and the publisher Paul Hamlyn back Mr Blair.
The spokeswoman defended the blind-trust system: "It is difficult, because we have to provide ourselves with the best possible office funding but if we identified donors we would be accused of acting on behalf of interests ... the Tories ... know who their paymasters are; they just don't tell the rest of us."
Mr Blair's office also receives funding from the taxpayer, known as Short Money, negotiated by Ted Short, Labour leader of the Commons and now Lord Glenamara, in the 1970s. This year Labour will receive pounds 1.5m, allocated by Mr Blair to his own as well as a number of other shadow-cabinet offices.