The problem is actually a lack of houses, full stop. An increasing population, with high levels of divorce, means trying to squeeze an ever-larger number of households into a limited amount of housing, which isn't growing at anything like the same rate. Added to this, the now huge student population has gobbled up whole streets of low-cost housing in many major towns and cities.
Obviously, making it uneconomical to hold a large stock of empty properties would release some property, and the only reason this isn't done is because some very wealthy people who are also donors to political parties deem it 'unacceptable', but that would have only a marginal impact.
The problem is made worse by the UK population's preference for a house with a garden and garage, so that large amounts of land are needed for x number of homes, even if they're cheek-by-jowl and with tiny rooms.