I mentioned the rental income more as an indicator of the 'utility' one derives from having use of the property during ownership. Alas, given how negligible the sum is in the scheme of things, it scarcely matters who assumes the burden.
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.