I've heard on the grapevine that EK might be looking to open a service to EDI as part of a general expansion to other european destinations, but I haven't heard anything about bases. But then again, I wouldn't be surprised if EK or EY do open a European base or maybe even a secondary hub, but I would seriously doubt that it would be at LHR.
I'd probably second guess somewhere less expensive, less congested and somewhat more passenger friendly. Maybe STN as LGW is too passenger unfriendly, and like T5 it's more shopping mall than point of departure.