The ally of Gordon Brown said it would be an "unhelpful distraction" if Mr Murphy remains in post ahead of next year's Holyrood elections, saying he said did not hold a democratic mandate after losing his Westminster seat.

Mr Rowley, a former General Secretary of the Scottish Labour Party, also said it would be a mistake for Mr Murphy's top team to remain in post, singling out chief of staff John McTernan. He added: "We have a leader in the Scottish Parliament" in an apparent show of support to the party's deputy leader, Kezia Dugdale.

A Scottish Labour spokesman described the resignation as "disappointing", adding that the task for the party going forward "is to work together to rebuild our movement and regain the trust of the people of Scotland."

Meanwhile, Unison's Labour Link, a key financial backer for the party, issued a statement in which it accepted that Scottish Labour's problems pre-dated the current leadership but also called for a "radical change in approach" following the devastating result in last week's general election which left the party with just one MP in its former heartland.

It added: "It is unprecedented for a party leader not to stand down after such a defeat, particularly when he loses his own seat. The campaign may have been energetic, but it lacked focus and clearly voters do not regard Jim Murphy as a credible messenger of Scottish Labour values.

"Scottish Labour has a limited period of time to reorganise itself to provide a credible challenge in the Scottish Parliament elections next year. There is very little time for a new leader to take the necessary actions, which require more than simply a change of leadership. Against that is the risk of further damage being done in next year's election if no change takes place.

"The current leader was elected fairly recently by a clear majority of members. However a majority of Unison Labour Link members did not share that view. Given that, we do not believe it is Unison's place to initiate a change in leadership. However, if there is a wider movement proposing change Unison Labour Link would not oppose it."

Elaine Smith, Labour MSP for Coatbridge and Chryston and deputy Presiding Officer, offered her backing to Mr Rowley and Neil Findlay, who quit the shadow cabinet at the weekend. She added: "They are putting loyalty to the Labour Party ahead of personal career or position and I think Jim Murphy should do likewise and step down as leader." She called for the reapplication of Labour principles rather than "chasing opinion polls and focus groups as we have been doing for the last five months."

Allies of Mr Murphy, who is likely to face a motion of no confidence at the party's Scottish Executive Committee on Saturday, pointed out that those publicly backing the apparent left-wing plot to oust the leader opposed his bid for the top job in the first place.

However, one prominent party figure indicated that backing for him remaining in power had become increasingly scarce, claiming that none of Glasgow's sitting MSPs or those already selected as 2016 Holyrood candidates had any faith in Mr Murphy carrying on.

The source added: "I've spoken to several and am aware of the views of the others. None believes their chances of remaining an MSP or being elected next year is bettered by Jim staying on.

"They are not inclined at this stage to put their heads above the parapet but also know they probably won't have to. There's enough mounting pressure on Jim without risk to themselves. It's probably in Jim's political interests to just go back to being Blairite Jim and stand somewhere in England."

However Gordon Matheson, leader of the Labour-run Glasgow City Council, said that Mr Murphy "must stay". He added: "My view this is absolutely not the time to be focusing on a divisive internal leadership election.

"Before the campaign Jim could not have been clearer about the scale of the challenge we face. No-one could have turned round in five months the fortunes of the Scottish Labour Party."