Is It Feasible To Connect Between London’s Heathrow & Gatwick Airports?

London is served by various airports, with the largest two being Heathrow (LHR) and Gatwick (LGW). While each of these offers direct links to a myriad of destinations worldwide,certain examples don't overlap. As such, it isn't implausible that passengers might have to connect between the two. But how feasible is this?