Property taxes (including inheritance taxes) can introduce huge inequalities of their own. Look at Italy for an example, where there are many beautiful villas left to go to ruin because the taxes were unaffordable for the families who owned them. Many landowners both in Britain and Italy are not really rich, particularly when they inherited them. Taxing them simply forces them off the land their families have owned for generations, and that's not really fair either.
You can buy whole Scottish estates, complete with castles and lochs and hundreds of square miles of wilderness, for less than the cost of a small flat in London. They aren't necessarily particularly viable economically, despite their size, and the owners aren't necessarily wealthy (though some are of course). They get put up for sale all the time for a good reason! They are a huge money sink.
