That actually sounds about right. The logic of fleecing those who can more afford it may not have good moral foundation. Its tempting, but can you explain how the borough gives more benefits to the rich than the poor? Possibly just the opposite.
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.