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. Some 600 people were living in the tower's 120 apartments.
May later announced that the public inquiry looking into the tragedy will report directly to her, the AP said. Protestors have called for her resignation, and she admits that the response should have been better in the initial hours after the 24-floor building was set ablaze.
Mr Cundy said: "Sadly, as of this morning, I am afraid to say there are now 79 people who we believe are now dead or missing and we have to presume they are dead".
"And we do know some of the people who advocated Brexit wanted there to be less fire and safety regulations in buildings". The police said the toll from the Grenfell Tower fire is expected to increase further.
Cundy said police had now managed to get to the top of the tower and had undertaken a first visual search for victims, ahead of later painstaking searches.
"There is considerable damage within Grenfell Tower", he said. Cundy has promised to share with relevant authorities any issues that need to be addressed immediately to protect public safety. He says "my heart goes out to those affected".
London's fire department says that the reason for the subway closure near the high-rise fire disaster is because of a "short-term risk of some debris falling onto the tracks".
Two neighbouring Tube lines are to be partly suspended into a second day amid safety concerns of debris falling on to the tracks.
London mayor Sadiq Khan has said that tower blocks in the city built during the 1960s and 1970s could be torn down following the Grenfell Tower fire. The package is also to include a commitment to ensure that all who lost their homes are re-housed as soon as possible near where they lived, temporary accommodation is paid for and that all victims are consulted during a public inquiry into the fire.
Major roads near the stricken building were open Saturday.
Mrs May met a group of victims, residents, volunteers and community leaders at a church close to the scene of the blaze, after earlier visiting survivors in hospital.
GRT said in a statement: "Work is taking place to assess the housing needs of all Grenfell Tower and Grenfell Walk families to identify suitable accommodation in Kensington and Chelsea and neighbouring boroughs".
The Grenfell Tower disaster is now the deadliest fire in mainland Britain since at least the turn of the last century.
"Put to the test, the United Kingdom has been resolute in the face of adversity". The queen was born in April but celebrates in June.
The latest figure included the 30 already confirmed to have died in the devastating fire on Wednesday.
More than 250 firefighters were called to tackle the blaze, which London Fire commissioner Dany Cotton described as "truly awful and shocking" for the level of devastation it caused.
The Government has also announced that a minute's silence will be held for the victims at 11am tomorrow.
The tragedy has provoked a huge response from nearby communities.
Other emergency service workers stood with their hands behind their backs and their helmets on the ground.