Check the app on landing. Personally I'd prpbably proceed to LHR because you'll obviously have a better idea of when you'll be there when you're there (to state the obvious) and your options for onward travel will be clearer.

I'd be looking at National Express timings for this evening on arrival at Gatwick, if you're over 2 hours you should be able to claim the cost of onboard wifi back. Also note down everything said about the fault as you may need that for UK261 compensation. I would also be scanning local hotels (in RAK) in case the flight is cancelled.