IAG isn''t an airline. There's no overlap between BA's LHR hub operation and Aer Lingus Regional routes to the UK. easyJet compete out of BFS with EI at BHD, that's not insubstatial. I don't see there being room for another turboprop operator.
BA have EZY competing on Scotland to London, I don't see how anyone actually taking on BA into LHR can win. It's just not viable, Virgin and latterly flybe just lost money as runners up. That doesn't mean London is a BA monopoly, just that out of LHR, it's obviously a strong (and likely unbeatable) offering IMHO.
Same goes for BA CityFlyer out of LCY, FR at STN and EZY out of LGW.