The council office demonstration came as angry people chased after May's auto, shouting "coward" after her meeting with fire victims at St Clements Church close to Grenfell Tower.
ACM has also been implicated in a high-rise fire in Melbourne's Docklands in 2014, and cladding rules have been tightened after apartment fires in Dubai.
Protesters stand in the lobby of Kensington town hall in west London, the headquarters of the Royal Borough of Kensington and Chelsea, demanding answers over the Grenfell Tower fire.
Given the unprecedented horror of the fire, and the potential implications for those responsible for the building and the regulations that apply to it, a descent into political points-scoring was sadly inevitable.
Firemen examine inside the Grenfell Tower in London as crews continue to damp down the deadly fire, Thursday, June 15, 2017.
BBC News reported Friday that about 40 additional people remain missing.
London Fire Commissioner Danny Cotton said: "Crews wearing breathing apparatus have been working tirelessly in extremely hard conditions to rescue people and to bring this major fire under control". But the focus has turned to renovations completed past year that added decorative touches to the building.
The cause of the fire, which has left at least 30 people dead, is yet to be determined, but the building's cladding is being blamed for the inferno's rapid spread.
"We just want to know they are safe", he told The Sun.
"I have never felt more accepted in this area than I was when I was helping, because they didn't care which side of the divide I came from".
The Sun newspaper said 65 people are now feared dead or missing in the fire.
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"It was a death trap and they knew it", one person shouted as demonstrators swelled outside the council building, with dozens going inside and clashing with police and security guards. "People have lost their lives, people have had their homes destroyed, they have fled for their lives with absolutely nothing".
She also pledged 5 million pounds ($6.39 million) of support, housing guarantees and help with access to bank accounts and cash.
The Labour leader said it is unacceptable for poor people and the homeless to be left looking for somewhere to live while land banking takes place in the area, adding properties should be "requisitioned if necessary".
May met victims privately at a central London hospital on Friday and had expressed her sorrow on television on Thursday after meeting emergency services personnel. Jeremy Corbyn arrived a little later, chatting to community activists, hugging distressed residents and promising to ensure that the truth about the fire comes out.
It is in no small part a response - solicited or otherwise - to the anguish, anger and demands for answers of a traumatised neighbourhood barely embarked on the long journey to coming to terms with the trauma.
London Police have launched an investigation to determine whether any crimes contributed to the blaze.
Pressed again on whether she had failed to understand the anger felt by the public, she said: "This was a bad tragedy that took place".
The Times reported that contractors are thought to have used panels with a polythene core for the Grenfell project.
Javid said inspections of similar buildings had been ordered, with particular attention to the modern cladding used to beautify and add an insulation layer to ageing concrete and steel structures.
The International Building Code calls for structures taller than 12 metres to use fire-resistant material.
Mr Javid said there was a lot of speculation about the cause of the fire and what allowed it to spread but that it could not be assumed "it's all about the cladding".
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