Footage from inside the gutted 24-storey building has been released, showing the extent of the damage caused by the blaze.
Metropolitan Police Commander Stuart Cundy said the conditions in the tower “verge on indescribable”, and warned of the potential “terrible reality” that some people may never be identified.
A minute’s silence will be held at 11am across all Government buildings to remember the people who lost their lives and all those affected by the fire.
As anger continued in the wake of the disaster, described by London Mayor Sadiq Khan as a “preventable accident”, the Government announced those left homeless will be given at least £5,500 from an emergency fund.
Residents will be given £500 in cash followed by a bank payment for the rest from Monday and the money will come from the £5 million fund announced by Theresa May on Friday.
While they welcomed the funding, a group of residents who met Mrs May in Downing Street at the weekend said they had not been consulted before the latest announcement, adding that it continued a “tendency to sideline residents’ views”.
Earlier the group, made up of survivors of the fire, evacuees from nearby buildings, volunteers and community leaders, criticised Kensington and Chelsea Tenant Management Organisation for its reaction to the disaster.
In a statement to the Press Association, they said: “With the exception of very few junior officers, the estate managers have been invisible in the aftermath of the tragedy.”
Releasing the footage of the flats, Mr Cundy said a figure for the latest number of people presumed dead will be given on Monday.
He said: “The conditions due to the fire damage verge on indescribable, which is why this will be such a lengthy operation taking weeks to complete.
“We must also prepare people for the terrible reality that some people may not be identified due to the intensity of the fire.”
He added: “Sadly that work leads me to believe that the number of people missing, but as yet unaccounted for has risen from yesterday’s figure of 58.”
Speaking after attending a church service near the tower block in west London on Sunday, Mr Khan said the local community was “frustrated” and “angry” in the wake of the blaze.
He said the atrocity followed “years of neglect from the council and successive governments”.
His remarks came as Nick Paget-Brown, the Tory leader of Kensington and Chelsea council, insisted officials were on the ground “very soon” after the fire broke out following criticism from Mrs May, who said the support given to residents was “not good enough”.
Mr Paget-Brown sidestepped questions over whether he felt guilty about the tragedy, telling BBC Radio 4’s The World At One: “I feel terrible about the whole position we find ourselves in. All I’m keen to say is there is an effective, co-ordinated relief effort on the ground and I’m sorry if people haven’t seen that.”
Meanwhile, a company involved in the renovation of the tower was forced to deny cladding on the building was banned in the UK after comments made by Chancellor Philip Hammond.
It was reported that the material used in the cladding covering Grenfell was Reynobond PE - a cheaper, more flammable version of two available options.
Appearing on the BBC’s Andrew Marr Show, Mr Hammond said: “My understanding is the cladding in question, this flammable cladding which is banned in Europe and the US, is also banned here.”
John Cowley, managing director of CEP Architectural Facades, which produced rainscreen panels and windows for Grenfell Tower’s cladding sub-contractor Harley Facades Ltd, said: “Reynobond PE is not banned in the UK.
“Current building regulations allow its use in both low-rise and high-rise structures.
“The key question now is whether the overall design of the building’s complete exterior was properly tested and subsequently signed off by the relevant authorities including the fire officer, building compliance officer and architect before commencement of the project.”