The meeting, convened by John Edmunds, general secretary of the GMB union, comes as senior Labour figures admitted that John Smith's plans for democratic reforms of the party structure face defeat at this year's annual conference.
Under Mr Smith's original plan, the unions would have no separate vote in electing the party leader or selecting parliamentary candidates. But, after a recent decision by the shopworkers' union, Usdaw, nearly all the big party affiliates are opposed to one-member one-vote.
Senior Labour figures believe Mr Smith may make concessions by committing himself to the creation of a voting role in constituencies for 'registered supporters' - trade unionists who are not full party members but who register their support. This scheme, which is backed by the GMB, has never been ruled out by Mr Smith even though it would dilute one-member one- vote. It would also be difficult to set it up in time for selection of candidates this year.
If this concession does not emerge the scene is set for deadlock. On Wednesday the unions, including the Transport Workers, National Union of Public Employees and Manufacturing Science Finance, will discuss ways to modify the old-style electoral college for candidate selection, in which they enjoy a 40 per cent block vote.
There will be a counter-proposal - unlikely to satisfy Mr Smith - for a 'cleaned-up electoral college', to prevent abuse of union influence in candidate selection, but preserve them a 30 per cent stake in candidate selection. Union secretaries are determined to block any change in their role in the selection of leader and deputy leader.
Mr Smith has begun exploring the possibility of using emergency ways to choose candidates if the unions carry out their threat to block moves to one-member one- vote in candidate selection, leaving the party with no constitutional means of choosing candidates this year.