As Chris states, tenants had the right to buy their houses from 1936, and small numbers were sold in the 60s and 70s.
The reason sales took off under Thatcher was because the houses were sold off vastly under their market value. A huge discount depending on the number of years the tenant had lived in the property, was attached to the price. In effect the housing stock was sold at many thousands of pounds under the market value.
The other downside was that councils were forbidden from using the proceeds of council house sales, to build new homes. The legacy of that is a housing shortage and very high house prices.