In the UK we have, not an 'owning a property tax', but instead a 'living in a property tax' (Council Tax). At one point there was an attempt to impose a 'living/breathing tax' (Poll Tax) but even we couldn't stomach that, and rioted until it was got rid of.

The US often has both "owning a property" and "living in a property" taxes; we call the latter an "HOA Fee".