Here's my experience....we've been in Northern England (Durham) for 1 1/2 years, and my children are 15 and 12. Adjustment wise, it was very tough for them last year. They are the only Americans in their schools and groups were already formed - and not too accepting to outsiders and there isn't much diversity. I'm sure that is way different to what you'd find in Southern England! Overall, I think education is what the Brits do best! I feel like the quality is high and there is a fair amount of emphasis put on the arts, languages, and physical ed. Of course, your kids will learn cricket and netball!!
With the ages of your children, I think it would be an easier adjustment, and maybe the groups won't be so set. In secondary, things do get pretty serious academically, and there's a fair amount of bullying that goes on. Even some of the teachers get away with cussing at the kids and callling them names....so I think the bullying atmosphere is kind of set by them, unfortunately.
Another thing I would think about is how long you're planning to be here. If it is going to be long enough for your kids to be in secondary here, you have to ask yourself if the high school experiences you had growing up (prom, sporting events, school spirit, etc.) are important, because you don't get that here. It's just pretty much a go to school, come home kind of thing!
But, I have to say I was surprised, because I ran the question of American School vs. British school past my kids, and they both said they figured the British school would win their vote at the moment! The big factor in that is all the neighborhood kids go to the local school, and they wouldn't really be able to know/play with them if they were to go to a private school.
Another thing I just thought about is parent involvement - what I found is that you're not as "needed" in the classroom as I was in the States, although some of that might be coming from my kids (ie. not passing on invitations to me!) because they are getting older!
Good luck with your move....with kids it can be tougher, but once they get settled it'll be easier for you guys!