You're missing the point, these are all rounding errors compared to the scale of the problem, and will only distract from the real issue. We need an overhaul of the entire housing system.
We need to raise £100 billion a year, put 2 million people to work and built 500,000 houses every single year. The money can be raised by bringing property taxes inline with most of the developed world (average OECD property tax revenue per total country's property wealth is about 2%, UK is about 0.50%). People need to be trained, lands will need to be renationalised, industries will need to be reignited.
This is not about empowering billionaires to do the right thing, time for that has passed. We need the government to interfere, and take on the role of the builder of last resort.
No, YOU are thinking small scale. The real scale of the problem means it's outside of the market forces, there are no tens of thousands of benevolent billionaires sitting on land waiting to build them if only they're allowed. If these benevolent land owners were going to do the right thing, they'd have done it decades ago. God knows the entire government, local or national, is in the pockets of the landowner class.
These landowners who have kept the land away to create supply shortages will need their lands to be renationalised, built on by a non-profit government project, and sold to first-time buyers at zero margin.
Renationalisation. Taking land from billionaires. Government built. Zero margin.
...and then you wake up from the dream and go make a coffee.