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Bristol Somali Community Association
Residents have accused a council of not doing enough to tackle repeated deliberate fires at a tower block.
The latest blaze at Haviland House in St Jude's, Bristol, on Sunday is thought to be the seventh in the past two months.
Abdihakin Asir from Bristol Somali Community Association said security measures promised by the council weren't working.
Bristol City Council has been asked to comment.
Avon and Somerset Police said a crime scene investigator and fire crews were trying to establish the cause of the latest blaze.
It started in a stairwell at about 01:00 BST and spread to a lift.
Homeless people sheltering in a doorway at the block and lighting fires to keep warm are thought to be the source of the problem.
Mr Asir said the fires were an ongoing problem at the flats and residents "don't feel safe".
"Last time we met a housing officer in that building, he said that they increased the security patrols - it's not working," he said.
"Residents are so worried that they think a similar incident to Grenfell may take place in that building unless the council do something.
"One resident said to us that the smoke came into their apartment. That itself is huge risk for that family and their children."
Avon and Somerset Police said house-to-house inquiries had been carried out.
"The Easton neighbourhood team will also be carrying out further reassurance work with the local community," it added.
Council housing officers met with the group after the last fire and said security patrols in the building had been increased.