@ThumbWitchesAbroad
When the council tax was introduced, the Tory run councils mostly had much cheaper council tax bills than Labour or Lib Dem run councils.
Wonder why...
Why? It's because Council Tax only represents about a quarter of local authorities' revenues. The rest (i.e. the vast majority) is doled out from central government.
This has several implications. First, even in the Gordon Brown years of opulent public spending the sort of thing that would happen is that central government would impose additional costs on local authorities in areas like social care, education, safeguarding and various other regulations, but not provide any additional central funding. This meant that council tax would have to rise four times higher than it should have done had central government paid its fair share, and for central government to claim it didn't raise taxes.
Second, it means that the dishing out of central government funding is politicised rather than done to any kind of fair formula. Central government funding to local authorities is where most of the austerity of the Cameron years actually hit. You'll be astonished to learn that it hit hardest in Labour-run councils (mine, which even by Labour standards is way out left of Looney Left, lost over 30% in a decade). This means that Council Tax skyrockets up without really making a dent in the shortfall, services are cut left right and centre, and Cameron/Osborne/Boris/Rishi can blame profligate Councils for it.
The whole stinking mess (by which I mean local government full stop, not just its finances) needs burning down and rebuilding from the bedrock up.
In Portugal, municipal taxes are based on the value of a property recorded in the land registry at the last change of ownership, adjusted for inflation. There are then a series of adjustments applied to take into account the property's particular characteristics - if you are more than a certain distance from a bus stop for example then your bill is adjusted down as you are deemed unable to benefit from the (council-subsidised) bus service. It seems much fairer to me.
For anyone tempted to under-declare the value of a property when it is purchased to reduce their annual council tax, capital gains tax is levied on all residential property gains unless you roll it into another residential property, so you get stung harder there when you try to realise your capital gain.