Interesting question. I had no idea this fare even existed.
If you go to
www.southernrailway.com and enter Heathrow, one of the options that comes up is Heathrow Rail. The fare is £39 single and various expensive return fares are also offered.
Quite clearly it is Heathrow Express that is offered (and not Heathrow Connect). It's not valid from Heathrow on the Piccadilly Line. You must travel to Paddington by Heathrow Express then by tube to Victoria.
From Victoria it is "Southern trains only" but that ought to allow travel on Gatwick Express, which is operated by Southern although you might be challenged; all connections offered by Southern on their website using this fare are on trains other than Gatwick Express.
Journey time is in the order of 1 hour 45 minutes.
If you make this journey again, consider taking Bus 285 (from T1/2/3) or 490 (T4/5) to Feltham station and the train to Clapham Junction, changing there for Gatwick.
Journey time is similar (depending on connections) and while the bus journey is not the best, no steps are involved during the entire journey and you can use an Oyster card to pay a reduced bus fare.
To save time, if you hold an Oyster card you can travel free to Hatton Cross by Piccadilly Line then take either bus from there to Feltham, but that may involve steps while exiting Hatton Cross station.
Via Feltham is very much cheaper (especially the off-peak fares) and avoids using the tube or going through Central London. When you board the bus, you can pay then ask the driver to let you board through the central doors with your suitcase. There are lifts at both Feltham and Clapham Junction.
In the opposite direction, i.e. to Heathrow, you can buy a Gatwick to Zones 1-6 Travelcard at £15.80 which will allow any (Southern) train to Clapham Junction then travel to Feltham and also cover the onward bus fare to Heathrow.
If you are making a return journey within one month the Feltham route is also very cost effective.
