Eric Pickles, the Communities Secretary, told The Daily Telegraph on Friday: “We are keen to remove tax and other regulatory obstacles to families having a live-in annexe for immediate relations. We should support homeowners who want to improve their properties and standard of living. These reforms should also play a role in increasing the housing supply.”

It was reported that hundreds of thousands of families could benefit, though the timing or detail of any change, which would probably require primary legislation, was not clear.

Labour said the policy idea was “decidedly peculiar” as annexes occupied by relatives who are either over 65, “mentally impaired”, or “substantially and permanently disabled” have not had to pay council tax since 1997.

Hilary Benn, the party’s communities spokesman, said: “This cynical spinning shows that, once again, the Tory-led government is over-claiming and under-delivering for our nation’s pensioners.

“This seems to be nothing more than an attempt to deflect attention from their housing crisis. We need to get building and get the economy moving again.”

No decision has yet been made on whether town halls would receive compensation from central government for income lost if fewer annexes paid council tax.