I'm not sure if this has been thought through clearly.
Gatwick would be owned by a separate company which would have to suitably distanced from both Easy & Virgin Management and Directors to satisfy competition rules.
This isn't a case of both airlines taking an equity stake in another airline, they're proposing taking on a major UK business with many existing customers and different types of businesses on ONE site who aren't going tolerate any crap.
If they do make a successful bid, to run Gatwick properly on a day to day basis they're going to have to appoint much stronger and more astute management and directors than currently exist at either airline.