The mass resignation, which wipes out the Labour majority in the east London borough for the first time in 25 years, was made in "protest over the continued cover-up of a child-abuse scandal".
The dispute centres on the case of a former Hackney child-care worker, Mark Trotter, who was on the point of being arrested on charges relating to paedophilia when he died of an Aids-related illness.
There were allegations that because Mr Trotter was a local Labour activist, Hackney covered up the case rather than trace children who might have been abused.
Rebel Labour councillors called for an independent inquiry into the case and though the local Labour leadership agreed to set up a properly constituted investigation, those councillors allege they were threatened with "gagging" disciplinary action for ignoring party procedures in cases of criminal allegations.
But with Conservative Party headquarters piling in to highlight the embarrassment over the affair among the national Labour Party, Terry Ashton, general secretary of the Greater London Labour Party, said: "These councillors have failed the people who elected them."
It was agreed at a party group meeting on Monday night, attended by some of yesterday's resigning rebels, that a motion for an inquiry should be debated at a council meeting tonight.
The group also agreed that the motion's wording should first be checked by the office of Hackney's chief executive and the Government's social services inspectorate to ensure that it was "completely water-tight".
One local party source - not involved in the long-standing internecine civil war being fought out within the Hackney council group - said last night: "Hackney is a political cess-pit which cannot be saved until after the next local elections."
Meanwhile, however, the Conservatives will exploit the disarray as evidence that a Tony Blair government might be tarred with the Hackney brush.
Eric Pickles, Tory party vice-chairman, said Labour's attitude to the abuse claims was disgraceful.
He pointed out that the Labour rebels had been calling for an inquiry and added: "Incredibly, the Labour leadership's response was to threaten disciplinary action against the councillors because of their demand for an inquiry.
"Attempting to muzzle their own councillors and to deny full scrutiny of the facts will only add to the public's fears."
The situation yet more complex last night when one of the "rebel" councillors wrote to Tony Elliston, the council's chief executive, retracting her resignation. Cynthia Thomas O'Garrow, who signed the rebels' resignation letter to Mr Elliston, gave no reason for her decision to resume the party whip.