Victims of the Grenfell tower fire could boycott the inquiry into the disaster if the proposed scope is not widened, campaigners have said.
Sir Martin Moore-Bick, who will lead the probe, had previously said he was "doubtful" the investigation would be far-reaching enough to satisfy those who survived the blaze.
The current proposals are for the inquiry to look at the events of June 14 - such as how the fire started and how it developed so rapidly - but calls have been made for the investigation to be broadened.
It comes as:
:: The Government said it will keep a "close eye" on Kensington and Chelsea Council as pressure builds for the troubled authority to be taken over by commissioners.
:: One Grenfell Tower resident claims she had her rent deduced from her bank account after the disaster.
:: It has emerged an executive from the company that made the insulation fitted to Grenfell Tower is an adviser to the Government on building regulations.
Yvette Williams, one of the organisers of the Justice 4 Grenfell campaign group, said Grenfell survivors and victims' families are "very, very angry" and want the "systemic issues" surrounding the fire to be looked at as part of the inquiry.
She told Sky News: "They cannot just look at 14 June, when that building became an inferno. They can't do that.
"If we don't get good terms of reference for the public inquiry and we don't get a wide remit so that those people can take responsibility for what they've done, then we won't participate in it."
It follows Labour leader Jeremy Corbyn writing to Prime Minister Theresa May, urging her to widen the scope of the public inquiry.
He has asked for a two-part inquiry, the first looking at specific issues around the fire in at the 24-storey building in Kensington, west London, and reporting back soon, with an additional second part "looking at the national issues".
Meanwhile, communities secretary Sajid Javid said it was "right" that council leader Nicholas Paget-Brown resigned following intense criticism of how the Grenfell Tower tragedy was handled.
Mr Javid said: "It is right the council leader stepped down given the initial response to the Grenfell tragedy.
"The process to select his successor will be independent of government, but we will be keeping a close eye on the situation. If we need to take further action, we won't hesitate to do so."
Outgoing leader Nicholas Paget-Brown said he had to share responsibility for "perceived failings", departing alongside deputy Rock Feilding-Mellen.
The council has now been hit by three high-profile resignations in the aftermath of the fire, with chief executive Nicholas Holgate also exiting.
The authority came under fire for its slow response to the disaster, in which at least 80 people are thought to have died.
The Labour Party launched a drive for the council to relinquish its handling of affairs until the crisis was brought under control, with a string of party figures weighing in.
London mayor Sadiq Khan, who welcomed the resignation, said the Government had "no option" but to appoint "untainted" commissioners who had "a genuine empathy for local people and the situation they face" to take over running the authority.
He said: "The council now needs to find a way to move forward and find a way to restore the confidence in that community.
"That can only be done with new leadership and a new approach that reaches out to residents who quite rightly feel desperately neglected.
"I ... feel the response from the council and subsequent breakdown in trust is so severe that there is now no alternative and the Government needs to step in quickly."
Commissioners were brought in to run Tower Hamlets Council in 2014 after a critical independent report into the council's award of grants and sale of properties under former mayor Lutfur Rahman.
Shadow housing secretary John Healey said the move would amount to "specific, immediate, obvious and necessary action", while shadow communities secretary Andrew Gwynne added the powers should be used to "get a grip on what has gone dreadfully wrong".
In his resignation statement, Mr Paget-Brown acknowledged the council had been criticised for "failing to answer all the questions that people have" but that the scale of the tragedy "was always going to mean that one borough alone would never have sufficient resources to respond to all the needs of the survivors and those made homeless, on its own".
Calls were also made for Kensington and Chelsea Council to be scrapped altogether, making way for a larger body.
Foreign Office minister Mark Field, a former Kensington councillor, suggested London should have bigger authorities so they are better-equipped to respond to major crises.
He told the Sunday Times: "I doubt that K&C, or any London authority, has the critical mass to deal with something like this.
"It raises questions about whether the model of London governance, with 33 unitary authorities, is really a sustainable model. Thirty-three does seem too many.
"You could look at the New York model, where they have five boroughs. I think that's what we will move towards."
Labour MP David Lammy, whose friend Khadija Saye died in the fire, indicated Sir Martin must work hard to maintain the confidence of victims.
"He is a white, upper-middle class man who I suspect has never, ever visited a tower block housing estate and certainly hasn't slept the night on the 20th floor of one," he told Sky News's Sophy Ridge On Sunday.
"I hope he would do that in the days ahead.
"The job is not just to be independent and judicious - I am sure he is eminently legally qualified, of course he is - it is also to be empathetic and walk with these people on this journey.
"To sit with them and understand that their lives were in the hands of the state and something badly, badly failed.
"It is a shame we couldn't find a woman to lead this inquiry or indeed an ethnic minority to lead the inquiry in 2017.
"I think the victims will also say to themselves: when push comes to shove, there are some powerful people here - contractors, sub-contractors, local authorities, governments - and they look like this judge. Whose side will he be on?
"He needs to get close to those victims and survivors very, very quickly and establish he is after the truth and he is fearless and independent and won't be swayed because he is part of the establishment."