The uk already has a fairly progressive property tax call stamp duty and many councils in the UK have property taxes (or at least our equivalent called council tax) for empty properties. The problem persists not because of billionaire investors but due to:

- Easy capital access in the form of cheap buy to let mortgages. Easy access to leverage mean property out performs pretty much every other investment and much of the middle class can afford it.

- Lack of regulation on tenancies. Very very easy to kick people out and up the rents.

- General shortage. The uk simply doesn't build enough houses. This is made worse by many jobs existing primarily in London / many graduates not realising that there are opportunities outside of London.