Only two people have formally complained to their local authority about being told to either sell their homes or pay up to £48,000 for repairs – but others have said that will not stop them considering legal action.
Extensions were built onto 380 council homes in the Low Hill area of Wolverhampton in the 1970s and 1980s.
But now that many are crumbling, the city council says the extensions, known as pods, are unsafe and need demolishing.
However, 32 of the extensions are attached to pods built onto homes that are now privately owned.
The council says it is unable to tear down the extensions at its own properties without affecting the privately-owned homes, so those must also come down.
Private owners have been told they face either selling their homes to the council at full market value or paying up to £48,000 for the work to be done, whether privately or through the authority.
Some who were outraged by the announcement have been encouraging others to lodge formal complaints with the council – the first step towards potentially taking legal action against the authority.
But today it emerged that only two of those affected have done so.
Sharon Rousell, who handed out complaint forms at a residents' meeting following the council's original announcement, said she was surprised that the number was so low, adding that she understood it to be higher.
She said: "I know of three, including me, who have complained."
She added: "There are still bound to be some of us prepared to look at legal action so it won't stop the rest of us.
"If people aren't filing complaints it doesn't necessarily mean they aren't bothering; they might have their reasons."
For those wishing to seek legal advice, the next step after lodging complaints with the council will be to approach the housing ombudsman.
The council, however, says it anticipates reaching an agreement with everyone involved and has encouraged the homeowners to seek independent legal advice.
The repairs are being carried out at the 260 properties owned by the council that have pod extensions.
Work has already begun at void and rented properties and the entire project is expected to take around two years, with the options put forward by the local authority currently being consulted on.
Council spokesman Gurdip Thandi said: "We have received two formal complaints from private residents following our consultation on options to rectify defective extensions to joined council and privately owned properties.
"These will be considered as part of the consultation process for this phase of works."