Speaking at the Welsh Labour conference in Swansea, John Edmonds, general secretary of the GMB general union, urged candidates to endorse a 'vote-winning' policy of full employment. Although Mr Edmonds declined to name senior politicians who might benefit from such strictures, his assertions will be seen by many in the labour movement as a shot across the bows of Tony Blair and Gordon Brown.
Both shadow ministers argue in favour of full employment, but trade unionists are more sceptical about their commitment to such a goal compared with other, more left-wing potential candidates such as Margaret Beckett - presently the acting leader - John Prescott and Robin Cook.
Mr Edmonds' union yesterday published the findings of an opinion poll which showed that 86 per cent of voters thought full employment was an important policy.
Another showed Labour could gain an 8.5 per cent swing from the Conservatives if it made full employment a major issue.
The 4.5 million trade unionists who pay the political levy would also be interested to hear the candidates' views on issues such as the minimum wage, employment and pension rights, and the role unions should play in the Labour Party.
Under the new electoral college which will determine John Smith's successor, levy payers will command one-third of the votes. The rest will be divided equally between party members in the constituencies, MPs and MEPs.
Mr Edmonds said: 'The GMB will encourage candidates to recognise this enormous test of opinion and reflect issues of concern to trade unionists in their campaign.'
One central issue in the debate which will be sparked by the GMB is precisely what is meant by 'full employment'. Mr Edmonds' aides argue that a figure of 3 per cent unemployment - compared with the present official figure of about 10 per cent - is the target.
Research for the GMB surveys was conducted before the death of Mr Smith and they were aimed at influencing the European elections. However the timing of their release means that at least one 'union baron' will be keen to influence the outcome of the Labour leadership election. One GMB source said that Mr Edmonds was simply 'drawing a line in the sand and saying don't cross it'.
Mr Edmonds, in common with other union leaders, has shown a marked reluctance to name any favoured candidate. The GMB executive will meet ahead of its annual congress in three weeks' time and will decide whether to recommend a 'ticket' for the leadership.
Bill Jordan, president of the Amalgamated Engineering and Electrical Union, said Labour already espoused a policy of full employment and senior party figures were all committed to it.
There was a need to avoid a 'personal dogfight' and there was also a need to elect a person who sounded like a leader and looked like a winner.