The meeting is unlikely to quell complaints that May has been slow to reach out to victims, despite her announcement of a $6.4 million emergency fund to help the displaced families.
The London Evening Standard reported that hundreds of activists marched to the town hall and gathered outside the building on Friday chanting: "We want justice".
"I'm able to say at this point in time at least 30 people have died as a result of this fire", he said.
Police Commander Stuart Cundy said the number of 58, which was based on reports from the public, may rise and includes the 30 deaths that have already been confirmed.
Police bundled the British premier into a waiting vehicle amid angry shouts of "coward" from protestors.
Police hold back crowds outside St Clement's Church in West London.
As the protesters sought to gain entry to an upper floor, police tried to bar their way. Police barred their way and scuffles broke out, a reporter said.
May met with hospitalized survivors Friday after coming under criticism for failing to meet with angry residents of the building earlier in the week.
However, Mr Green would not say whether other tower blocks would be retrofitted with sprinkler systems in light of the tragedy. "We could put out children to bed and know they would get up in the morning".
EU Parliament negotiator wants Brexit clarity from London soon
The Conservatives have been locked in talks with the socially conservative party founded by the late Ian Paisley since the results of the election emerged last week.
Protesters demanding justice for the victims of the Grenfell Tower inferno have stormed Kensington Town Hall.
According to media reports, the cladding had a plastic core and was similar to that used by high-rise buildings in France, the United Arab Emirates and Australia, which had also suffered fires that spread. She later called for a full public inquiry into the catastrophe. Her government is also due to launch hard Brexit talks with the European Union on Monday.
"Meet the victims!" one person yelled as Leadsom was interviewed on Sky News. "We owe that to the families, to the people who have lost loved ones, friends and the homes in which they lived". "One woman told me she had escaped in only her top and underwear".
She said earlier that the national mood is somber but that Britain is resolute in the face of adversity.
"She should have been there with the residents".
The latest figures from NHS England show that 24 people are still being treated in hospitals across London, of whom 12 remain in critical care.
Residents have also criticised the local authority as many of those left homeless struggle to find out where they will be rehoused in the medium term.
As the search for missing people enters its third day, anger among the residents was still palpable but they are less keen to talk as television cameras swarm the scene.
However, Foreign Secretary Boris Johnson took to Facebook to attack Labour politicians for "political game playing", defending his record regarding the fire service as mayor of London between 2008-2016.
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