For example the text books would say that you can fly at 2100ft without clearance if CAS is from ground to 2000ft, however, good manners would suggest that you still look for a clearance
Actually, no, they have no authority to issue a clearance in that case
It's good manners to call them up because (Brize Norton is a classic case, where I have flown many times overhead) they often have traffic about in the overlaying Class G, and they may indeed like to direct you about a bit.
It's one of those bizzare things. You could overfly Brize at 3600ft, non-radio, non-transponder, and I guess they have to assume you are
above their airspace.