At least 30 people died in a fire.
Mrs May, already under pressure after a botched snap election, is facing widespread criticism for her response to the blaze.
She has promised to set up a public inquiry and pledged 5 million pounds to help the victims.
Separately, hundreds of protesters stormed the local town hall chanting: "We want justice."
May has outlined a series of measures to help those left homeless by the devastating fire which engulfed the 24-storey apartment block on Wednesday.
But fury has grown in the local community at what people say is the slow response from authorities to the fire and a failure to inform families and friends about the fate of loved ones.
Local residents also say they are angry that their safety concerns had been ignored and that people had been told to stay in their flats in the event of a fire.
May, who on Thursday met emergency services at the fire site but did not meet locals, visited residents, volunteers and community leaders at a nearby church on Friday and was rushed away afterwards by police as an angry crowd outside shouted "Coward" and "You're not wanted".
A couple of miles away in west London, several hundred protesters stormed Kensington and Chelsea council town hall.
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