Mr Khan echoed their point, saying: «People are angry, not simply at the poor response in the days afterwards from the council and the government, but at the years of neglect from the council.
«There’s a feeling that the council and government don’t understand their concerns and don’t care.»
He added: «People in this community are sick to death of platitudes from politicians.»
Kensington and Chelsea Council leader Nicholas Paget-Brown said he understood residents’ anger and that the authority itself wanted to know why the fire had started and spread so quickly.
He added that the disaster was too big for one authority to handle alone and it was inaccurate to suggest his council was not present on the ground or working with other authorities.
The government has sent in a team of civil servants to bolster the relief effort. They were spotted in high-visibility jackets in the area on Sunday afternoon.
Details of how the government’s £5m emergency fund have been outlined, including:
Funding will be made available for people staying in temporary accommodation
A discretionary fund is available to help meet funeral costs
There will also be funding for legal representation for residents involved in the public inquiry
An extra £1.5m will pay for mental health support for the emergency services
Mrs May said: «My government will continue to do absolutely everything possible to help all of those affected through the difficult days, weeks, months and years ahead.»
A newly-established «Grenfell Fire Response Team» has been set up to lead the relief effort, which will include a 24-hour operation at the Westway Sports Centre.
The new team is made up of local and central government, the Red Cross, the Metropolitan Police and the London Fire Brigade.
Eleanor Kelly, chief executive of Southwark Council, said speeding up the rehousing process would be the main priority.
The Red Cross has been asked to increase its role and and its staff will be part of teams allocated to every household affected by the fire, as well as meeting bereaved relatives as they arrive at airports.
The charity’s helpline — 0800 4589472 — is now the central point of contact for all people affected.
Mrs Kelly added in a statement: «There is nothing we can say that will blunt the feeling of loss and anger.
«But I hope the new team and this package of support will start to get those affected by this tragedy the urgent assistance from the authorities they need.»
Earlier, writing in the Observer, Mr Khan had suggested that high-rise tower blocks dating from the 1960s and 1970s could be torn down in the wake of the fire, which he said may well be the «defining outcome of this tragedy».
Chancellor Philip Hammond told BBC’s Andrew Marr Show that a criminal investigation would examine whether building regulations had been breached when the block was refurbished.
Labour leader Jeremy Corbyn told ITV’s Peston on Sunday that the council had seemed to «lack the resources to deal with a crisis of this magnitude», despite being the country’s «wealthiest borough».
Meanwhile, Labour MP David Lammy, whose friend Khadija Saye is among the dead, has called for all documents relating to the refurbishment and management of Grenfell Tower to be protected.
Questions continue to be asked about why the fire spread so quickly, amid suggestions new cladding fitted during a recent overhaul could have been to blame.
The prime minister has come in for a barrage of criticism over her response to the disaster.
She was jeered on a visit to the North Kensington estate on Friday, and protesters marching on Friday and Saturday called for her resignation.