Does the Tax go by council and Civil usage?
Is this how its branded?
Council tax banding is based on the value of your house in its current in April 1991... Crock of shite if you ask me and I'm afraid it's a very sore subject

Yes, you are correct -- on both counts. It's a PITA for the Council Tax people too AFAIK -- but that's what Maggie brought in and what we are all stuck with for now!
If you are convinced you should be in a lower band it costs nothing to appeal --- might take a few months to get sorted, but will be back dated if you win. BTW -- the appeal is dealt with by the Valuation Office ... they don't get the money so have no axe to grind if your bill is reduced! ( which is why they are doing it and not the councils).
Being ex MOD is very similar to ex council house -- in 1991 their values were artificially low -- hence low bands now.
The actual pounds and pence you pay ( as opposed to the band) will depend on how spendthrift your council is. Band c in a lot of London Boroughs pay less than a band c here, because 1) the boroughs are more careful with their money than our council is and 2) the population is more densely packed so more to share the bills between !!!