Councils are not empowered (and don't currently have the expertise) to develop land. Instead, they have to scape some of the profit from private developments in the form of S106, or CIL...
Councils and other Registered Social Landlords [Housing Associations] can and do develop land for social housing in conjunction with private contractors.
The problem is that building land is worth too much to private developers so they can rarely make the maths work.
If local need can be proved, social housing can be built outside normal planning rules, for example on green belt land. This is working OK in certain parts of the countryside, where there is a lot of land which can be worth 10x or 20x more as social housing land than for agriculture, but not in cities and we mainly need houses in cities.