Not gonna happen. BMI are the Star Alliance feed into Heathrow. BA feed their long haul from the regions. They might need to tighten the frequencies but there's no way Heathrow will lose it's domestic routes as they are the arteries to the international services. That would be silly.
Do you seriously want to arrive at 5am from the Far East and get on a bus to an different airport?
Quite the contrary - with the new northern SHORT runway, we might see a limited return of the likes of Inverness and others. Be good to get the Highlands linked back in again and join up the dots.