Tenants evacuated from a tower block over fire safety fears claim they face being burdened by extra rent due to the building's tarnished reputation.
Two residents who share a flat at the Chalcots Estate in Camden said they could be forced to move out after a promised rent reimbursement from the council was hit by delays.
They claimed the cash was needed after news coverage of the building's safety crisis left it "stigmatised as a fire trap" and made it difficult to attract someone to fill a recently vacated room.
Others living in the building were also said to have moved out after the estate's four tower blocks were evacuated on June 23 when its cladding was found to be flammable.
Jermaine Joseph, 37, who lives in Taplow Tower on the estate with a flatmate, said Camden Council had yet to deliver on an offer to repay rent.
He told the Press Association: "We've had people coming to see but they are not taking it. It is kind of comical trying to show somebody around a potential flat when the building has been temporarily evacuated.
"The reason one girl decided not to take the place was because of the situation, which puts us in a rather unfair situation because if we cannot find someone within a few weeks we are going to be stuck paying a third more on our rent and potentially still not having our rent reimbursement.
"We are not using it to throw a party - we are using it to fill the hole that is left as a result of all of this."
His flatmate, Dave, 40, who did not want to give his surname, added: "If we don't get any progress we are going to have to find somewhere else to live - we have now been stigmatised as a fire trap."
The two men rent their property from a landlord, rather than the council, but the authority offered to cover rent for the period they were displaced.
In a document given to residents after the evacuation, Camden Council said: "If you are a private tenant, we will reimburse your rent for the duration you are evacuated from your home."
But Mr Joseph said that, despite spending a month in a hotel room, his attempts to recoup money had not succeeded. He reported having to send over information about his claim repeatedly after being told there was no record of previous calls.
"I have got in the habit of contacting them every day and following up and following up and following up, it is extremely frustrating," he said.
"It has got to the point now that it feels like they genuinely do not care."
Nationwide testing of the material used to clad high-rise towers was launched following the deadly inferno at Grenfell Tower, in which at least 80 people died.
A spokesman for Camden Council said: "With nearly 3,000 people evacuated from the Chalcots Estate the council is working through a large number of financial reimbursement claims for those who self-funded their accommodation during the period they were away from their homes.
"We apologise for the length of time this process is taking but it is a complex operation, particularly when claims are being made by sub-tenants of leaseholders.
"It is vital that we not only receive receipts for the cost, but also proof of tenancy and proof of respective financial rent transactions. The council has a duty to the tax payer to carry out that due diligence.
"Equally, we acknowledge that we have a duty to ensure that residents are inconvenienced as little as possible during this difficult time and any resident that wishes to raise concerns about the implications of how long the process is taking can contact us on 0207 974 4444 (option 7) or email email@example.com."