The money the local authority gains from the sale is then ringfenced and can only be used to build new social housing.
That's not my recollection and Wikipedia seems to agree with me.
Half the proceeds of the sales were paid to the local authorities, but the government restricted authorities' use of most of the money to reducing their debt until it was cleared rather than spending it on building more homes. The effect was to reduce the council housing stock, especially in areas where property prices were high, such as London and the south-east of England.
Quite. Add to this that turning arbitrary selections of council housing into private property didn't simplify or reduce the cost-per-home of maintaining the rest; did the reverse, in fact.
That's not my recollection and Wikipedia seems to agree with me.