The Transport and General Workers' Union has sent out a strident letter in support of Mr Livingstone and has refused to accept a timetable for balloting its members.
The union has ignored pleas from Labour chiefs, who are trying to deliver the party's nomination to Frank Dobson, to hold ballots at the same time as the vote by party members. The unions are likely to vote decisively in favour of Mr Livingstone.
Party apparatchiks are worried that any substantial vote for the left- winger would create a bandwagon in his favour.
However, the TGWU, of which the Prime Minister is a member, will complete its vote before the ballot of Labour Party members in London and it is thought the result is bound to leak out.
The votes by trade unionists are part of an electoral college also made up of party members and MPs.
Much to the irritation of New Labour in a letter to TGWU members in London, Barry Camfield, the union's regional secretary, makes clear the organisation's strong support for Mr Livingstone and does not even mention Mr Dobson or Glenda Jackson.
Pointedly, the letter says the union is endorsing Mr Livingstone because it trusts him. Mr Camfield writes that the left- winger believes in accountability and has often attended the union's regional committee to give a parliamentary report.
"He is regarded as a man of principle who has always fought for London and London's interests. I ask that London T & G members give Ken Livingstone an overwhelming vote of confidence," he writes.
A pro-Dobson union source said: "We had an agreement that we would ballot at the same time, but they seemed to have jumped the gun."
The result of the TGWU vote will be available from 6 January, but all the results are not due to be announced until 16 February.Reuse content