I know that poll tax was deeply unpopular, but why? It replaced a system based on houses' rateable value, which was pretty much the same as council tax, and that's not fair either.
Currently, there is no incentive for people to improve their lifestyle, as as soon as they do (eg by buying a house with more space for children) they are penalised. CT is just another form of means-test, which works against social mobility. Also, as the charge is per household rather than per individual it means that some pay far more than others for access to the same services. I think that we should all pay for services (eg education or leisure centres) whether we use them or not, to spread the cost for those who do use them, but a family of (say) four adults in a household should pay twice as much as a couple, as there are twice as many people with access to the services in their area, twice as much rubbish to be collected and so on.
IMO, taxing everyone fairly in the first place, then leaving people with the rest of their income to spend (or save) as they wish without penalty is the fairest way to do it. The charge could be one bill for the household or one for each member, but it should be based on the number of adults living there, not the notional value of the house in 1990 or whenever the bandings took place.