Commander Stuart Cundy of the Metropolitan Police confirmed that he was "so grateful" that five people who had been missing after the fire on Wednesday 14 June had been found over the past few days.
Mr Cundy said the death toll may still change, but not as significantly as it has in recent days.
One firefighter, in his black protective suit with FIRE emblazoned in yellow on the back, embraced a distraught woman who had photos of a missing person printed on her top.
A total of £202,000 of government money has been handed out to 180 families who were directly affected by the Grenfell Tower fire.
As the group of Grenfell residents and volunteers passed through the gates of Downing Street, protesters shouted angry chants about the Prime Minister and wore white ribbons as a sign of solidarity.
A statement said: "We plan to house residents of Grenfell Tower as locally as we can".
London's Metropolitan Police confirmed Friday they had launched a criminal investigation into the incident.
Obesità: oltre 4 milioni di morti nel mondo, Africa compresa
E sempre più persone perdono la vita a causa di questi problemi: in un anno circa 4 milioni muoiono a causa dell'eccesso di peso . Secondo gli autori, "i risultati documentano una crisi di salute pubblica crescente e inquietante".
The meeting is unlikely to quell complaints that May has been slow to reach out to fire survivors, despite her announcement of a $6.4 million emergency fund to help the displaced families.
May said after the meeting Saturday that there have been "huge frustrations" in the community as people tried to get information.
Theresa May said: 'As we continue to respond to the needs of the community, our focus is on ensuring that all of those affected by this unimaginable tragedy get the right support as quickly as possible. British health authorities say that 19 fire survivors are still being treated at London hospitals, and 10 of them remain in critical condition.
Police said they are using the INTERPOL Disaster Victim Identification Standards to identify the deceased.
A solemn Queen Elizabeth II marked a minute of silence Saturday for victims of the London high-rise inferno that killed at least 30 people as exhausted firefighters continued their grim search for more bodies.
There is simmering anger in the multi-ethnic north Kensington area hit by the blaze, and public fury has been directed at senior government figures, including May, who was jeered Friday after she visited.
Mrs May has announced a public inquiry into the fire, which will be fast-tracked. Officials and UK Chancellor Philip Hammond have indicated that the external rain-screen cladding believed to be the cause of the rapid spread of the fire at the Grenfell Tower may have been banned under building regulations in the UK.