After a disastrous attempt at a poll tax, the system was renamed "council tax" for residential property. It's banded, so very high value property is under taxed. e.g. http://www.theguardian.com/money/2012/mar/09/council-tax-in-...
We tried that. It didn't work.
You can own a £10m property in the borough, earning upwards of £1m per year in rental income and appreciation, and only have to pay £2k to the local council.
Meanwhile, those living in the absolute worst accommodation in the borough still have to pay £711.19.
Note that, in theory, a secondary function of the council tax should be to prevent habitable properties being left unoccupied for extended periods of time.
Unfortunately when the tax amounts to a rounding error on the ROI for a property, it is completely ineffectual. Hence the large number of empty 'investment' properties in London, further inflating an already overheated property market.
Furthermore, there is no moral right to ineritance.
Why should someone who's lived in a property for decades be taxed out of their house just because the area they live in has become a desirable area?
To your actual point, to tax someone out of a £10m home in London today the council tax rate would have to be increased many thousands of times over. That is not a realistic danger.
This policy is seeing a resurgence of popular support in the form of the 'Mansion tax', but really all we need is a more equitable council tax.