A buffer zone guarded by metal railings and lines of police officers greeted the demonstrators, who continued to chant at the gates outside the Prime Minister's official residence.
May, already under pressure after a botched snap election, is facing widespread criticism for her response to the blaze.
She said in her message on Saturday: "Today is traditionally a day of celebration".
The queen marked her official birthday Saturday by saying Britain remains "resolute in the face of adversity" after the horrendous fire and recent extremist attacks in London and Manchester.
Recovery: Members of the emergency services in the middle floors.
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.
British authorities are launching a criminal investigation into the London apartment building fire - as the death toll from the blaze has almost doubled, to 30.
Some people then left the building though others remained inside.
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It was the first time since the world ranking began in 1986 that the top three players missed the cut in any major. Thomas is no stranger to low scores. "That means I'm a part of history", Thomas told reporters.
June. 18: The Police has announced that the fifty-eight people who are still missing after the Grenfell Tower fire, are being presumed dead. It does not matter why you have not told us, what is important is that we know you are safe.
Mr Cundy vowed police "will get to the answer of what has happened and why", adding: " If criminal offences have been committed it is us who will investigate that".
Among concerns previously been raised by people in the wake of the fire was the lack of a centralised missing person list and worries over where Grenfell residents will be rehoused. May had been criticized for refusing to meet any residents or their families during a Thursday visit to the site, reportedly due to "security concerns".
On Friday she was met with shouts of "coward" and "shame on you" when she emerged from a Kensington church where, under a heavy police presence she had met with victims and community leaders.
Activists and local residents held demonstrations at the borough's town hall, London's Oxford Street, the United Kingdom home office, the BBC, and the prime minister's official residence at Number 10 Downing Street to vent their frustrations.
"The prime minister is this morning chairing a cross-government meeting to ensure everything possible is being done to support those affected by the Grenfell tragedy", the spokesman said.
Mayor of London Sadiq Khan, who was at the meeting, said he used it as a "crucial opportunity for me to make clear to the Government" what the residents need. He says it will take weeks or longer to recover and identify all the dead at the charred building.
The cause of the fire is still unknown but "there is nothing to suggest the fire was started deliberately", London police said in a Friday statement. "We know that there are still bodies of those who died inside the building and we want to return those people to their families as soon as we possibly can".
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