Grenfell Tower fire campaigners have said they want a wide-ranging public inquiry, as the deadline for submissions on its scope closes.
Justice 4 Grenfell said it wanted an examination of local and national social housing policy and whether it "increased risks to residents."
About 300 suggestions are expected to have been received by the consultation.
Meanwhile, a further three inquests have been opened, bringing the total number of identified victims to 48.
Coroner Dr Fiona Wilcox opened, adjourned and suspended inquests into the deaths of Fatima Choukair, 11, Firdaws Hashim, 12, and Hashim Kedir, 44.
At least 80 people are believed to have died in the blaze on 14 June.
The fire in the 24-storey block started in a Hotpoint fridge freezer and destroyed 151 homes, both in the tower and surrounding areas.
Questions were raised in the aftermath of the disaster about the cladding used on Grenfell and other buildings. More than 100 buildings have failed the latest fire safety tests set in the wake of the fire.
Retired Court of Appeal judge Sir Martin Moore-Bick, who is leading the inquiry into the blaze, promised to consider a broad range of evidence when he launched the public consultation into the terms of reference - which closed at 17:00 BST - in July.
Local community members were initially given a week to give their feedback, but the deadline was extended twice.
Sir Martin is due to send his draft terms of reference to Prime Minister Theresa May next week.
She will then decide what the scope of the inquiry should be and respond the week after.
The inquiry is due to start in September. Sir Martin has previously said an interim report could be produced within a year.
He has previously faced calls to resign from residents, while Labour MP David Lammy said he was a "white, upper-middle class man" who had "never" visited a tower block housing estate and should not have been appointed.
At the inquests
By Alex Murray, BBC News
Having attended several times now, the inquests follow a grimly familiar format. Although brief, each session has been traumatic for those present.
No matter how many times we have heard them, the phrases never lose the power of their horrific narrative: "Human remains recovered from...", "identified by DNA" or "dental records"; "Presumed cause of death: One A" "Inhalation of fire fumes", "consistent with the effects of fire".
Relatives have struggled with the emotions of this formal and public moment of grief in the silence of the court.
Today, three relatives of Hashim Kedir each raised a single clenched hand to their mouth as the presumed cause of death, "consistent with the effects of fire", was read out.
The gesture may be small, but the significance is deeply felt.
With at least 32 individuals still to be identified and that process "becoming increasingly difficult", there are still many who will have to pass through this horrible moment.
Justice 4 Grenfell said it had submitted six suggestions for the terms of reference.
It said one of the main purposes of the inquiry should include restoring public confidence in the safety of social housing and the "competence, ability and willingness of public authorities" to regulate it.
The group said it wanted the inquiry to investigate Kensington and Chelsea Council and government departments, including the Home Office, the Department for Communities and Local Government and 10 Downing Street.
It said: "The inquiry must uncover the correspondence and documents within these departments that go to the heart of the failed housing and social policies that caused or exacerbated the fire, along with the appalling response in the aftermath.
"The inquiry should seek and obtain internal communications between government ministers, MPs, councillors and civil servants on matters relating to the Grenfell Tower disaster and the issues related to it. "
The group said it wanted a diverse group of people on the panel "to ensure that the experiences of the wide range of people affected by the fire are included at the earliest opportunity".
"This is essential to ensure community trust, confidence, and the continued and full participation of survivors and the bereaved families in the inquiry process," it said.
'We want change'
Christos Fairbairn, who escaped from the 15th floor and is struggling to sleep, said the inquiry must consider the mental health implications of what happened.
"It's difficult to come to terms with the fact that you live in a block, you meet people every day, you say hello to them and these are the same people who died and it's their whole families," he told the BBC.
Chairman of the nearby Bramley House residents association, Samia Badani, said: "Having spoken to hundreds of people, they want the inquiry to deal with the relationship between the residents and the local authority and tenant management organisation.
"We'd be very disappointed if it was narrowed down on the causes of the fire.
"We want real change, and unless they understand that relationship between public bodies and residents is flawed, there is no hope of this changing."
Meanwhile, tributes have been paid to Hashim Kedir and his 12-year-old daughter Firdaws, whose inquests were opened and adjourned at Westminster Coroner's Court.
A family statement described Mr Kedir as a "soft-hearted and generous brother and uncle" who was "intelligent, smart, hardworking, hilarious, and caring".
His daughter was "our intelligent, wise, eloquent and beautiful niece and cousin", her family said.
"You were so smart and mature for your age that everybody had a lot to say about the type of future you were going to have; the future that was stolen from you," the statement said.