I've been wondering this for a while actually. Do they have American History classes? We have European History so I wouldn't see why they wouldn't but is the Revolutionary War a sore subject still? I talked to someone from England and they knew nothing of the subject. I'd think they'd know at least SOMETHING about it.
This is in no way a complete answer, but here's two example GCSE syllabus for History in the UK. GCSEs are exams students take at the age of 15/16:
http://www.aqa.org.uk/subjects/history/gcse/history-8145/specification-at-a-glance
You'll see that "British America, 1713–83: empire and revolution" is an option in the second, but as one of five options available. So it is taught in places, but it's not required.
The American Revolution not being taught in the UK isn't because it's a sore subject, but because it didn't really have a very huge effect back home. There's a great AskHistorians thread about British civilian reaction to the loss of the war that goes into far more detail, but in short, there was no huge political upheaval, and the two countries reconciled and traded etc. pretty quickly. And from the perspective of history education, you have to remember that "Britain loses a colony" happened a lot of times, so it makes sense you wouldn't cover them all, especially when your list of "things to cover" goes all the way back to Roman Britain.
Obviously it's an absolutely crucial event in US history, but it's more difficult to argue that it is significant enough that it must be studied in the context of British history.
(as an aside, European History is studied in America because it's the root of American History as well, not to mention that it goes back a lot further. European students do study American history, but as it relates to them - the Great Depression, for example, had a worldwide impact and is often studied)