I'm fortunate enough to live in a Labour-controlled council, and they have an active plan to build more social housing:
The council aims to build 400 new council homes for social rent by 2027, constructed to high energy-efficiency standards known as PassivHaus to reduce running costs. Construction has begun on the first phase, with 75 homes underway across three sites* ... supported by funding from the Mayor of London’s Affordable Homes Programme.
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X: 36 one- and two-bedroom apartments.
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Y: 21 homes.
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Z: 18 apartments and larger family homes.
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A: Additional sites include land at xxx
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Acquisition of Social Housing
To further address the shortage, the council has approved the acquisition of 146 social homes at the former x site. This decision followed criticism of developer St William, who initially failed to deliver affordable housing due to viability concerns. These homes will be transferred to the council’s Housing Revenue Account within two to three years, bringing the total number of council-owned social homes to 221.
It's still not enough, of course, but at least they're doing it.
*deleted the actual places as don't want to be too outing!