The bands came into play in something like 1992. They were based on an approximate valuation of your property at that time. I would google the subject to find out the exact dates and what the valuation thresholds were.
If you look on the Nationwide Building society web site there is a house price calculator. You can put in two dates, one when you knew the value and the other, a date that you want a valuation for. If you had a valuation recently, stab in those details and ask for a valuation when the bandings were determined. That should give you a rough idea.
I have no idea how they arrived at the valuations when property was close to the thresholds. There are some errors e.g. a friend of mine doubled the size of his terraced house, but they classified him at the pre-extension value. Lucky him, until they realise their mistake.
The amount of council tax you pay does not corrulate with how nice an area is. There are some councils who preside over really crappy areas that spend spend spend - social housing, social issues etc etc. Another posh area might have a lot less of this and so council tax would be cheaper. It just comes down to what the local authority is used to spending, not neccessarily how nice the area is.