The UK does not have property taxes. The figure given is presumably council tax, which is a fixed fee per household, vaguely based on the house's supposed value. The highest council tax band is quite low; i pay £2,000 per year, and my flat is worth a lot less than $20m.
This is correct about rented properties, but not about empty ones.
Empty properties can attract a discounted rate of council tax, but are only exempt under certain circumstances (resident in prison/hospital, house unlivable).
Long-term empty properties can even attract a higher rate of council tax.
That last part is simply incorrect; Councils have a time limit on whether empty properties are exempt from council tax. Also, there's an extra 50% penalty if it's been empty/unfurnished for 2 years or more:
https://www.gov.uk/council-tax/second-homes-and-empty-proper...
