We have now established beyond reasonable doubt that the so-called home builders, Barratts, Taylor Wimpey and the like are nothing of the sort, see e.g. here and here.
The construction is carried out by subcontractors and Barratts et al are a cartel of land bankers who dribble a few new homes onto the market each year in order to realize part of the value of their "investment portfolio" (as Taylor Wimpey describe their land bank) without depressing its overall value.
The official stat's for completions in public and private sectors show that private sector completions have averaged 167,000 a year since 1960 (once austerity had ended and the economy was going again); and until Thatcher more or less shut down construction in the public sector in 1980, an average of 167,000 new units of social housing were built.
It's actually difficult to pin down the role of NIMBYs in all this (as despicable as their motives usually are); they are clearly behind the fall in construction of social housing, and the biggest cheerleaders for selling it off at huge discounts, but it's doubtful whether they have any influence on how many homes the land bankers dribble onto the market.