Brands like BA BE even Bmi all good ideas, if possible of course but let's think long term would BA be suitable for non BA destinations like Carlisle or another non London airport that Stobart could buy.
Moreover, BA may like to pursue a franchise operation in the future there are few regional operators left and BA might at some point in time go after this eve though it has given up on same in the UK before ....
Can't see BA being interested in SEN bearing in mind their operation at neighbouring LCY.
As for thin domestic and near-abroad routes, perhaps the only interst for BA would be to feed the longhaul network at LHR. That's not possible at present and won't be unless and until it expands.
Under those circumstances, would imagine that BA would have an arrangement with one or more of the smaller carriers (code share, through ticketing, etc.), as it does not have small enough aircraft and an A319 once/day won't cut it (frequency required).
Perhaps BE could be a candidate for this as BA is already a part-owner of it, but it's very far in the future if at all!
BD regional on the other hand might very well be a candidate for SEN operations, as they currently have no operations in the southeast and small aircraft suitable for thin routes to/from SEN. Let's face it, they're not going back to LHR any time soon!