The government currently spends somewhere between £17b - £24b a year subsiding rent / paying housing benefit (different reports are giving different figures).
The average cost to build a new house is betwee. £1500-£3000 per m2, with the average house in the UK measuring 76m2 this gives an average cost of between £114k - £228k per house.
This means the government could build between 74,000 - 210,000 new "average" houses a year, if they weren't paying out any housing benefit (obviously that's not going to happen overnight)
The average annual payment to someone in receipt of housing benefit is around £4980 pa or £415 pcm, meaning there is between 3.4m-4.8m people claiming housing benefit. The average rent in the UK is £1175, meaning tenants in private rentals who receive housing benefit are paying c.£760 pcm themselves to a private landlord.
Now on to the point of this, the government could have taken that £42.5b they've spent on a vanity project trainline that only benefits a tiny fraction of the county and instead built between 186,00-372,000 new houses.
They then could have moved 186k-372k people from private rentals to the new houses, stopped the housing benefit payments to them and generated some additional income from the tenants share of rent. Hell, they could even lower the rent so tenants in the new properties only paid £500pcm instead of £760.
This would save £910m-£1.8b in year 1 in housing benefits and generate between £93m-£186m in rental payments (using my £500pcm figure), which could be reinvested.
They could then take the further £70b earmarked for HS2 and build a further 307k -£614k new homes and do the same. Thus would refuce the total number of housing benefit recipients by c.500k-980k, saving between £2.5b-£4.8b pa, and generating between £250m -£490m pa in rental payments.
Again reinvest the money saved into building new properties and within a decade or so you've reached the point where there's no need to be paying out housing benefit.
This would also bring the rental market under control and potentially reduce house prices too, and ensure people living in social housing were living in good properies/conditions. You also don't just have to build new houses, building flats or buying existing properties could probably get you to this point much quicker.
Obviously it's not as black and white as that as you'll have ongoing O&M costs and what not, but the lack of affordable housing and all the issues surrounding it is solely down to government choice.
Ask yourself this, would it be more beneficial to the country to have up to a million new, well-insulated, desirable and affordable houses or a one passenger train line that saves 20 minutes when traveling from London to Birminghan or Manchester?