Maggie tried to revise the system back in the 90's and look where it got her.
She did and and made the mistake of trying to revise it to a fair basis i.e. everyone paid the same for the council services they received based on the number of people in the house irrespective of the house value.
The riots had nothing to do with rationality.
The current council tax is a misnomer in that it's not a tax to pay for council services received, it's a property tax based on property value. Even if it's an outdated value, council tax is still a very progressive tax with band H paying 3 times more than band A. labour want to make it even more progressive.
Overall, tax is getting more progressive all the time even under the conservatives. In recent years we have had huge reductions in the pensions life time allowance and dividend tax allowance both of which are a tax on savings that hit the relatively well off not just the super rich.