At least 12 people died after the huge fire destroyed the block in north Kensington, west London, where flames could still be seen burning more than a day on from the disaster.
The commissioner said: "Tragically now we are not expecting to find anyone else alive. The severity and the heat of the fire would mean it is an absolute miracle for anyone to be left alive."
She said there are still "unknown numbers" of people in the building.
More than Â£1 million has been raised to help those affected as fire tore through the 24-storey building while volunteers and charities helped feed and shelter people who could not return to their homes overnight.
Ms Cotton said the upper floors of the building are still to be searched.
"Sadly we do anticipate the death toll will rise - we haven't done our searches of the top floors yet," she told reporters at the scene.
Prime Minister Theresa May is expected to visit the scene of the tragedy later on Thursday to speak with emergency services and ensure that they have the resources they need to deal with the situation.
The London Fire Brigade (LFB) said a ruptured gas main in the block had to be isolated before fire crews were able to put the blaze out and bring it under control by 1.14am.
A 40 metre aerial appliance was brought in from Surrey Fire and Rescue Service to help with this.
Ms Cotton said the number of people who are unaccounted for is still unknown as some may have got out by themselves or gone into other flats.
The cause of the fire is still being investigated.
A large number of material has been taken away for sampling in detailed searches of the flats as evidence is collected along with identification of the people who live in the flats.
She said "in quite a short period of time" investigators will try to pinpoint the cause of the fire.
Firefighters who worked in intense heat and under falling debris have suffered nine minor injuries, ranging from burns, smoke inhalation and heat exhaustion but the potential psychological damage to them could be a future concern.
Ms Cotton suggested it "will take weeks before this building is truly cleared and searched properly" as parts of it still need to be shored up and there is a risk of falling debris.
Residents' groups have claimed they voiced concerns about the safety of the building, which had been recently refurbished, while those who escaped complained their fire alarms had not been set off by the blaze.
One focus for the investigation will be the building's cladding, which TV architect George Clarke said may have accelerated the blaze.
Mr Clarke, who lives locally and appears on Channel 4's Amazing Spaces, told BBC's Newsnight: "I saw those cladding panels, the cladding on the outside and the insulation was just peeling off, like you'd peel a banana.
"It was fully on fire.
"I could see the flames behind, there's a new cladding system put on the outsides that looks like a new skin, there's an air gap an insulation behind that, to me that looks like a fantastic chimney for the fire to rage around."
Grenfell Tower, built in 1974, was recently refurbished at a cost of Â£8.6 million, with work completed in May last year.
Kensington and Chelsea Council admitted it had received complaints over the works, after a residents' action group said its warnings about safety had fallen on "deaf ears".
A blog post from Grenfell Action Group in November said "only a catastrophic event" would expose the concerns residents had.
The group said there was one entry and exit to the tower during improvement works and it had issues with evacuation procedures.
Concerns had also been raised about exposed gas pipes weeks before the devastating blaze.
Rydon, the firm that carried out the refurbishment work, said the project "met all required building regulations", in its latest statement following the fire.
But a line stating the project had met all "fire regulation and health and safety standards", which was included in an earlier release, had disappeared.
Harley Facades Limited (HFL), who completed the Grenfell Tower refurbishment which included installing the exterior cladding, said its thoughts were with the residents and their families and they will fully support and cooperate with the investigations.