A group of rebel MPs have begun soliciting signatures for a round robin letter calling for Gordon Brown to step down, which they plan to hand to the prime minister after the results of the local and European elections have come in on Monday morning.

The Guardian has learned there are reports that the backbenchers think they can reach 70 or 80 signatories, crucial within Labour party rules that require 20% of the parliamentary party to mount a challenge – 70 MPs.

The current plan is that no hard copy of the letter should exist for fear of leaks. Instead, a "tree" of backbenchers, extending through the 350-strong parliamentary party, is soliciting signatories.

Under the plan, an email address would be handed out to which sympathetic MPs are to send an email saying they support a single-sentence statement that they would like Brown to stand down.

There had been plans for the letter to go "live" at 10am on Friday morning but it now appears that those at the head of the movement are considering delaying their strike until Monday morning.

There were even claims yesterday that the letter could be delivered to Downing Street by the end of today.

Some backbenchers have seen the letter and are not signing it on account of a perception that the names already on the list are "too leftwing".

The rebels are deeply irritated that news of the plot has emerged, knowing that the charge of disloyalty ahead of the elections will dissuade as many as a score of backbenchers from joining their ranks.

At the beginning of the week, 50 MPs were said to have agreed to sign the letter with the ambition that the number would rise to 80 before it was sent to Brown.

There had been a deep fear among those who want Brown to go that the exposure of any "plot" would endanger the results of this week's elections and that Downing Street would crush the rebellion.

Rebels calculated that the "disloyalty factor" could dissuade a crucial 20-30 extra names, and that feeling is magnified this afternoon.

The revelation came as Hazel Blears, the communities secretary, delivered another devastating blow to Brown's leadership by unexpectedly resigning ahead of tomorrow's polling day. Her announcement came 24 hours after Jacqui Smith, the home secretary, quit, and amid continuing rumours about the fate of the chancellor, Alistair Darling.

David Cameron told Brown at prime minister's question time that his "ability to command the cabinet has simply disappeared". He said the prime minister was "in denial" about the scale of the crisis facing him.

Nick Clegg, the Liberal Democrat leader, joined in the attack, telling Brown that his government was in "meltdown".