I've taken my kids (now 7, 5 and 2) back and forth to Scotland nearly every year. We always go in the summer (where it is daylight until nearly midnight so they don't have sleep cues anyway) so we don't change the kids' sleep schedule. We keep them on EST for the whole trip. It is a bit of a hassle but worth it in the long run.
Nursing makes it so much easier to feed them when they are small, too.
Another helpful hint when they are older is to never allow TV at home but always allow them unlimited movies and games on the flight. All of my kids have always been so good on long flights because of that! They look forward to the plane ride! (They get to have big cookies and juice, too).
Make sure to look in the "wrong" direction when you cross streets in the UK. People always forget that and there are near constant accidents with pedestrians.
Have fun!