unite union
Unite general secretary Sharon Graham also urged to PM to ditch the "cruel" policy of taking winter fuel payments off millions of pensioners.
Pro-Jeremy Corbyn campaign group Momentum condemned the party leader's "fiscal conservatism".
Sharon Graham says the former leader would win his seat of Islington North if he chose to stand.
Ambulance workers and nurses' strikes set to go ahead later this month after the government and unions fail to reach a pay agreement.
Sharon Graham accused David Lammy of launching a "direct attack" on British Airways workers.
The union has been overtaken by Unison as the biggest in the country.
Steve Turner wants to replace Harriet Harman when she stands down in Camberwell and Peckham.
Leftwinger backed by the Socialist Workers Party signals end of Len McCluskey era
Moderates hope for a ‘clean sweep’. But Howard Beckett thinks he’s got the momentum.
Guidelines for general secretary election make it harder to get on ballot paper, MPs warn.