It's amazing no one else has thought about funding local services, i.e. Libraries etc, by actually taxing richer people more.
I know this might sound a bit mad, but I think we may well be at a point whereby things like tax bands and to an extent tax rates should be sorted from the data/stats, rather than being used as much as a political football.
One of the main points of tax is to redistribute wealth by taking from those with a lot to provide services for those at the bottom who can't afford them.
So if you have the info on income levels, you could look at, say, the 50th percentile and the top 10% and work out the difference and however many times more the earnings are at the 90th percentile is some sort of multiplier for the upper tax rate, and also sets the income level at which it is paid. If society is fairer then that upper rate will automatically be low. If we have a huge discrepancy it will be large. It automatically reflects the society we're living in.
Tax free personal allowance should be set at the amount people need to pay rent/mortgage, bills and food. Then you can see what percentile that relates to and maybe work out a basic rate from that as well. Plus should you choose you can add in further tax bands based on percentiles, for example a super rich tax on the top 1% compared to what they have over the top 10%.
I know this doesn't cover the big issue of accumulated wealth (I think something along the lines of treating inheritance as income rather than a separate IHT could be a possibility), but would need access to all the data (and a lot of free time!) to turn it into a detailed, potentially workable solution.