You could link both airports by train using existing track but it would take a very convoluted routing through Acton and Kensington Olympa and then on already overcrowded track to LGW.

Given that the Gatwick Express is likely to be canned, I would say that air pax using rail links isn't top of the priority list for the Department of Transport right now.

And how many people actually transfer between the two airports? Not that many I suspect.