The fact that this county tax is paid by the leaseholder not the property owner is what was missing from the context. (And it boggles my mind why this is the case.)
England is run by landowners who are really hostile to the idea of property tax. The last big attempt at reforming the ancient "council rates" system in the 90s converted it to a per-person "Poll Tax". This was incredibly unpopular, widely boycotted, and resulted in riots. The system was dialled back to a system based on the value of the property in 1991, paid by the occupiers, with exemptions for students and empty properties, and a 25% discount for people living alone (mostly pensioners).
Empty properties are not always exempted. It's up to the council. Sometimes they are, sometimes there's a discount, sometimes there's no discount, sometimes people have to pay extra for empty properties.
