"We want justice!", "Shame on you!", and "Killers!", the protesters shouted, as they scuffled with security guards in the lobby of the building, AFP reporters said.
Hundreds of people protested outside the Kensington and Chelsea town hall holding handmade signs reading "Justice for Grenfell".
The protesters also held up pictures of those still unaccounted for and now feared dead.
Police have said 30 people are confirmed as having lost their lives in the blaze, with more than 70 unaccounted for. Local residents have accused police of hiding the true toll.
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"I have friends in the tower and they are not telling us anything," Salwa Buamani, 25, told AFP.
"We are not given information about our loved ones," she added.
"We are not here to trouble people. We just want answers," said Buamani, who came to the protest with her three-year-old niece on her shoulders.