The BA flight arrives at 7:20. The EZY flight departs at 9:20. Gatwick can be efficient but I have had plenty of experience of long haul arrivals where bags have taken 45-60 minutes to arrive. If it has ever been quicker it has only been by a matter of minutes. EZY bag drop closes 60 minutes before departure.

So you have up to about 15 minutes to play with. I agree that transfers between the two terminals is efficient, but 10 minutes from carousel to train, 5 minutes on the transit and 5 minutes walk to the bag drop is going to make this very difficult.