The catchment area if an individual airport is so difficult to geographically define these days as the UK is a relatively small country and so many airports within easy reach of so many. My nearest airport is BHX (I live in Worcester) and I always research flights from there first but in the past 18 months I've also flown from MAN, BRS, STN and LTN none of which I consider to be in their catchment areas based on where I live. My decision to fly from these airports varied - mostly to do with flight times, frequency of flights and days I needed to travel and destination.
BRS strength is that it is the only relatively easily reached 'major' airport for South Wales, Somerset, Devon and Cornwall (relatively affluent areas). BHX being in the middle of the UK doesn't have claim to an individual area to mop up passengers from and yes, big parts of its geographically close populated areas are very deprived.
BRS on the other hand (like BHX) also suffers from the proximity of LHR, particularly for those living in Wiltshire and Berkshire its as easy to get to LHR as BRS both driving and on public transport.
I would wager it's also just as easy to get to BHX from Cheltenham and Gloucester as to BRS. If working properly you can get from Cheltenham to BHX by train in just over an hour much the same as catching the train to Temple Meads then the bus to BRS . As for road access to BRS, we all know how bad that is!
I wonder if easyJet will see some leakage of pax north of Bristol to BHX?