I guess it's just lack of supply

Supply isn't the problem as there are over 600,000 empty properties in the UK (last time I checked)
The problem is with the current distribution system. Absent owners, deceased owners with no will or beneficiary listed and of course the blood sucking developers land banking plots of land up and down the country and to a lesser degree investment property bought by foreign investors.
There is no shortage of housing just a broken system that allowed things to get this bad