Surely the poll tax works how you want, you'd be paying half what your two person household next door pays.
It certainly sounds that way, doesn't it?
I think a lot of people seem to think that houses with multiple adults in them are rolling in it and have maybe even deliberately chosen it that way in order to score themselves a bargain on their council tax.
A great many of them will include adult children who would love to move out, but just cannot afford it. Charging them an additional tax for the 'privilege' of not being able to afford to move out and live independently of their parents would merely serve to hold them up even longer before they can do so.
Also, even if people have chosen to live in multi-adult households when they could afford not to, is that not a good thing for the environment and more efficient use of limited housing stock? Leaving aside the circumstances of relationships and opportunities (or lack thereof) that have led to somebody living alone (or at least as the sole adult), in pure terms of good use of resources, they are not using their dwelling as efficiently as they could.
We had the recent thread about whether people in council houses should be forced to downsize once their children have grown up and moved out, to enable more efficient use of their big home, and many were criticising people as selfish for not doing so. In fact, however small your house or flat, there aren't many dwellings that couldn't accommodate a couple rather than just a single person - but obviously, nobody is suggesting that the council/government should allocate single people romantic partners to live with!
If we take the scenario of a single adult living alone in a large, high-band house, there's always going to be the starkly opposing viewpoints, where the resident objects to having to pay such a lot of money to X council when there's only one of them (and they don't have kids to use the schools, don't use the library etc.), whilst from an efficiency pov, they're 'wasting' a much-too-large house and so arguably should be actively disincentivised/punished for doing so.