If BA wants a presence on any of the routes that BMed currently flies, I imagine that they will need to fund this from within their own fleet and slots. GB isn't exactly flush with Heathrow slots and it is questionable as to whether many of the routes would financially work if flown from LGW.
Equally, some routes are constrained under the bilateral agreements with the overseas countries, and so there would not be room for BA, GB or anyone to enter certain routes alongside BMed if BMed's services remain in place with whatever name down the side of the 'plane. From memory, anyone wanting to launch services to Baku, Alexandria, Beirut, Tehran, Almaty, Ekaterinburg, Khartoum and Damascus would have problems as BMed uses the full quota of frequencies and rights available for UK carriers on its own.
Personally, I'd think that any prospect of GB having a headlong rush onto the BMed routes is pretty unlikely for the above reasons plus the rationale that if BMed has lost a fortune on many routes in the last 12 months, GB may well be wondering if they could do any better.