> In the UK, the equivalent tax on housing is council tax

Council tax is difficult to compare to a percentage based property tax - the band based system means people in super valuable homes pay virtually nothing, at least relative to the value of the property, and each of the ~8 bands pays a fixed fee - once in the max band the tax stays the same no matter how valuable the home.

This is especially acute in places like Scotland, where the top band kicks in at anything over 212,000 and hasn't been adjusted since 1991... Essentially any new build starter home in many places will automatically be in the top band and taxed the same as some dude who bought a castle for millions.

Personally I've never thought of council tax as a property tax, even if the bands superficially are linked to it- the link to underlying property values is so broken now.

My first rented flat outta college was taxed at the highest band, and I sure wasn't rich then. It's widely argued to be a very regressive form of taxation - its opponents indeed argue it should be replaced with an actual property tax.