I'm old, but not so old that I don't remember flying when I was kindergarden age. For 4 and 7 year olds, the flight should be a delight: you get a few cartoons at the start of the flight (I assume you're travelling economy), some nice lady gives you food in a strange package on a tray, and my parents kept giving me lots of books filled with different activities (connect-the-dots, mazes, and so on).
Yes, an eleven-hour flight is a long time even for an adult, and it may be difficult to keep an active child entertained. Like many have already said, the east-bound flight is the easier one, since it usually involves dinner and sleep. I'd say one important tip both east-bound and west-bound would be to try to keep their energy level down; no naps before getting on the plane, for example, and it might be a good idea to keep the candies, cokes and other high-energy eatables at a minimum.
You already know what your children like. Do each of them have a favorite book, one that they're looking forward to reading? Save it for the trip. Do they like movies or computer games? Take some along. And the idea of having a fall-back bag of small gifts is great, especially if it can lead to activity-time at their seats.
And yes, your children will absolutely love England!
