BA's Gatwick base is a complicated matter; average yield is much lower than at Heathrow, and the slots are much less expensive than those of Heathrow. If we're expecting a multi-year depression in aviation, then BA could easily centralise on Heathrow in part just to ensure they can make use of all the slots they currently own to avoid losing them. I don't think anyone is expecting the short haul services to holiday destinations to disappear: the expectation is very much they'll move to Heathrow, precisely for the sake of the slots.
I think if it's going to be really tough they are better off focusing on Heathrow - that way they can ensure they keep their competition out of their main hub. The slots which aren't getting used for services to the United States etc can be filled with more short-haul leisure routes.
I wonder what is a worse outcome, scaling down Gatwick and leaving business to rivals or having those rivals turn up at Heathrow. I'm not sure BA (or Aer Lingus) would be too keen on say Ryanair launching Heathrow - Dublin!!
If Gatwick loses the bulk of BA, Virgin and maybe Norwegian too (?) then it's going to be interesting to see who their main clients will be moving forward, not many airlines are planning expansion right now but I could see easyJet acquiring more slots at Gatwick as well as Wizzair and/or Ryanair being interested in building up more of a presence. I wonder if Gatwick will become more like Stansted or Luton being dominated by low-cost taffic in the long run.