Demonstrators pushed their way through an automatic door shouting 'We want justice!' and 'Killers!' as they clashed with security guards in the lobby. A larger crowd of people remained outside.
"If there are other buildings which have that risky cladding then immediate action needs to be taken in a matter of weeks, or months - not in a couple of years", he added.
"I drove up to see the building, which is only around the corner from me", he said.
While the disaster has prompted an outpouring of generosity, there was also fury at the authorities as the charred tower was cast as a deadly symbol of a divided society.
While PM May called for the public inquiry, she was also criticised for her visit to the fire scene on Thursday, which did not include speaking to any of the survivors of the tragic incident.
Protesters storm Kensington Town Hall after the fatal fire.
Queen Elizabeth II and Prince William visited an aid distribution site and were meeting with volunteers.
With many dozens of people still unaccounted for, people have been told to brace themselves for the death toll to rise.
Her decision came as politicians, community leaders and residents asked a simple question: "How in the 21st century can people perish in their own homes in one of the wealthiest boroughs in Britain?"
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The bodies of 12 people have been recovered and are at a mortuary, including one person who died after being taken to a hospital.
Anger and frustration mounted in the London neighbourhood stunned by the tragedy as relatives and friends of the missing made increasingly desperate appeals for information.
"As the Mayor of London, I will continue to fight alongside this community to ensure they get the support and answers they deserve and justice done", Khan wrote.
Hundreds of demonstrators gather for the protest.
Planning documents detailing the recent refurbishment of the block did not refer to a type of fire barrier that safety experts said must be used when high-rise blocks are re-clad. A massive fire engulfed a 27-storey apartment building in west London early Wednesday.
Whole families are said to be among the missing, including Bassem Choukeir, his wife Nadia, her mother Sariyya and the couple's three daughters Mirna, Fatmeh and Zaynab.
The paper also said that the last full assessment of fire risks for the building was in December 2015, before the refurbishment was completed a year ago.
London police said an investigation, led by a detective from its homicide and major crime unit, would examine whether criminal offences had been committed although they said there was nothing to suggest the fire was started deliberately.
"The recovery of victims from inside the building is enormously challenging, but it is our absolute priority above everything else to recover and identify the victims and let the families know", Metropolitan Police Commander Stuart Cundy said.
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