yggdrasil, that is no less fair than the current system where every household regardless of its how many people are in it and regardless income of income.
A lot of people who are retired are living in houses, that maybe quite small, but are still in higher Council tax brackets and now have far less income than when they were both in work, probably cannot afford to move, but equally struggle to pay their rapidly rising council tax.
A poll tax can be easily adapted to people's income. Let the Councils set a tax rate, which is payed through PAYE, with how much of the standard amount you pay raised or lowered in accordance with your highest tax rate. There could be a separate much lower rate for those on benefits.