I haven't flown through Gatwick, but I've gone through LHR more than once. There's a cursory security check when you get off the plane, but the line can take a few minutes. Then you walk a bit and go through passport control (another potential line), then another security check, very very very thorough, which can mean another wait in line. I don't go through passport control since I am in transit to another country, so I'm a little hazy on that. Then you have to get to your gate. Terminal 5 is big. You'll see overhead signs with the time it takes to get to your departure area. It can be 20 minutes. The website Harold posted claims it takes 60 minutes, using a 6.15 arrival and 7.55 departure. I assume that is from the arrival area to the departure area. Remember that a 6.15 landing time is not being in the terminal at 6.15. Even if your plane gets to the gate at 6.15, it takes a few minutes to attach the sleeve and start getting passengers off the plane. If you aren't in first or business or priority coach (or whatever they call it now), you'll be among the many people waiting for all those people sitting in front of you to move their butts. Remember that a 7.55 departure is not the same as being at the departure gate at 7.55. In my experience gates close at least 10-15 minutes before departure. It's possible that you won't have any landing delays or lines in the airport. According to the website, you only need to go through customs if you have something to declare. On your way home, you go through passport control in Europe and passport control and customs in NY.
Be sure to get your boarding passes for your connecting flights when you check in for the first leg. If you have checked luggage, ask for the bags to be tagged "short connection" and check that the correct airport code is on the tags.