Heathrow to Gatwick:
By Train
There's no direct train service between the airports. You can take the rail and Underground (Subway/The Tube) through central London. Travel by Heathrow Express to Paddington (a 15-minute trip from terminals 2, 3, 4, and 5). From Paddington, take the Circle Line to Victoria Station (a 15-minute trip) and connect to Gatwick via the Gatwick Express (about 30-minutes). The whole trip will cost about £40 pounds one way.
Alternatively, you can travel by The Tube from any of the 5 Heathrow terminals to Green Park (a 45-minute trip) and then from Green Park to Victoria Station (a two-minute trip). From Victoria Station, connect to Gatwick via the Gatwick Express (a 30-minute trip). The whole trip costs about £20 one way.
On days like Boxing Day (December 26) the Gatwick Express isn't running, you'll need to make alternative transportation arrangements. If you have mobility issues, if you're traveling with small children or if you have lots of luggage, take comfort in knowing that both routes offer easy step-free access.