The flats on Ekin Road have been branded "substandard" with mould and damp.
The Save Ekin Road group has called on Cambridge City Council to rehouse families living in "near uninhabitable" conditions.
The city council has said it cannot immediately rehouse tenants, but said anyone with concerns about damp and mould should get in contact.
Plans to refurbish or totally redevelop Ekin Road are still being considered.
The campaigners say the "vast majority" of people living in the flats want them taken down, but the 32 semi-detached houses in the estate don't need demolishing.
The city council says a dialogue with the tenants is ongoing.
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