Realistically the only way BA can continue LGW short-haul in the long term is if the feed from these services to their long-haul flights is good enough. BA currently fly several times a day to the likes of MAN, GLA, EDI, AMS from Heathrow, Gatwick and City airports, surely this isn't economical? If Gatwick long-haul could be profitable without a feed (which it is for Virgin), it would be much better to just run short-haul flights to LCY for business and Heathrow for connecting. Any leisure routes currently run out of LGW that are worth keeping could easily be transferred to LHR or LCY as appropriate.
As for the competition with Easyjet, I wouldn't have thought BA would be too concerned with Easyjet having a monopoly over LGW short-haul would they? After all, Gatwick is primarily a O/D leisure airport, it will not have much impact on their core business at Heathrow.