LON-EDI is already aggresively served across all of the major London airports by BA, easyJet, flybe and once again Ryanair. So it's not a BA monopoly, the problem is LHR is high cost and if BMI can't so with STAR ALLIANCE connectivty and Virgin with their high brand awareness bled red, then the only *likely* option would by EZY and that would only be in an expanded three runway scenario.
So in the medium term, no one, certainly no one likely to make money.