The leader of Britain’s biggest union has turned his fire on moderate members of the Labour party and demanded they elect a new leader who will champion “organised labour”.

Len McCluskey, general secretary of Unite, threatened to withdraw his union’s multi-million pound backing for the party unless picked the “correct leader”.

The Times reports that he also said that Unite in Scotland could even switch its support to the Scottish National Party in a veiled threat to outgoing leader Jim Murphy. Mr Murphy stood down this weekend, hitting out at McCluskey’s “destructive behaviour”, calling him the “kiss of death” for the party.

“We cannot have our leaders selected or deselected by the grudges and grievances of one prominent man. The leader of Scottish Labour does not serve at the grace of Len McCluskey, and the next leader of the UK Labour party should not be picked by [him],” Murphy said.

McCluskey hit back, accusing Murphy of “arrogance”, adding: “He represented the ideology that has completely alienated [voters] . . . not just in the election, not just in the [independence] referendum, but for years.”

His intervention has stoked a war within Labour, with moderates saying the party must not repeat the mistake of allowing the unions to choose the next leader. Ed Miliband won the leadership in 2010, narrowly beating his brother David, thanks to union support.

Speaking to BBC Radio 5 Live, McCluskey said: “It’s essential that the correct leader emerges and that there’s a genuine debate about the direction we’re going in. It is the challenge of the Labour party to demonstrate that they are the voice of ordinary working people, that they are the voice of organised labour. If they do that in a way that enthuses us, then I don’t believe that the mountain that’s ahead of us is unclimbable.

“But it’s up to them. If they don’t, if they kind of inject more disillusionment in the party, then the pressure will grow from our members to rethink. It’s certainly already growing in Scotland.”

Harriet Harman, acting Labour leader, will today try to reassure moderates that the unions will not have too much say over who becomes next leader after the party introduced new rules for leadership elections.

“Last time the unions communicated directly with many of their members, sending them ballot papers with accompanying ­material only mentioning one candidate,” she will say. “The winner of this election is not going to be the choice of the unions or any single ­section or faction of the Labour party. He or she is going to be the choice of the ­Labour party.”