A number of residents were treated for smoke inhalation after the fire was started at flats in Milton Mount Avenue, Pound Hill, at around 2.15am on Saturday.
The building was left badly smoke-damaged but residents say Crawley Borough Council has not acted quickly enough to clear up the damage to floors, walls and ceilings.
And Mark Morrish, who has lived in the flats since 1996, said he feared another fire, asking: “Is this another Grenfell?”
He said builders who were installing new pipes in the flats had left ‘combustible items’ in a communal area.
Last year, hundreds of residents were evacuated from the flats and put up in hotels following a major gas leak.
Fire crews from Crawley, Haywards Heath, Horsham,Turners Hill and Surrey attended Saturday’s fire.
A spokesperson for West Sussex Fire & Rescue Service said: "Upon arrival the ground floor and first floor was found to be smoke logged and firefighters wearing breathing apparatus used hose reels, jets and thermal imaging cameras to extinguish the fire.
"The premises was then ventilated to clear the smoke.
"A number of people at the scene were treated for smoke inhalation and were left in the care of South East Coast Ambulance Service.”
Crawley Borough Council says it is now organising a meeting with residents to discuss any concerns.
A spokesperson said: “We were distressed to hear of the arson attack at Milton Mount and glad that nobody was hurt.
"This was an incredibly dangerous thing to do and if anyone has any information about this serious crime we’d urge them to call the police on 101.
“We helped Sussex Police and West Sussex Fire and Rescue Service with their investigations and, along with our contractors, had limited access at the time of the incident.
"The fire service has since undertaken a visit to the site by a Fire Safety Officer and based on their observations at the time, it appears that the smoke seals on the fire doors functioned correctly.
"Further investigation into the circumstances of the incident are being carried out.
“In undertaking the major works at Milton Mount, the council, the principal contractor and principal designer agreed that building materials should not be stored on site.
"We have since discovered that a sub-contractor had left some materials in a localised area (not where the fire took place).
"This matter has been addressed with the sub-contractor, a ‘toolbox’ talk took place today and a health and safety advisor will attend the site on Thursday August 4.
“Our insurers have given the go ahead for us to progress with cleaning without site inspection to avoid further delays.
"Therefore, contractors will begin work today (Wednesday August 3) on clearing the walls and ceiling in preparation for redecorating, a quotation for redecoration has been submitted to the insurer for their consideration and approval.
“We are currently organising a meeting between council officers and Milton Mount residents to discuss any concerns around the incident.
"We would like to remind residents of all our blocks of flats that items must not be left in any communal areas and residents must ensure fire doors and entrances remain closed.”