Our first trip to England was mostly to London, but we also took a 3 day tour out to the Cotswolds, Oxford, Laycock, Chepstow Castle and a few other places I can't think of at the moment. It was a Harry Potter tour, which worked well since mom and dad got to see the architecture and our then 10-year old got to see Hogworts.
The tour "coach" itself only held about 10-11 passengers, so it was a small group. The hotels we stayed at weren't anything wonderful, but they weren't bad either, and the food was good for both breakfast and dinner. We were on our own for lunches.
Because it was a small tour group, didn't cover that much territory (relatively speaking) and the group got on well, we enjoyed ourselves. Even our son. There was another 12-year old boy on the tour (Harry Potter, after all) and a teenaged girl, but the kids didn't do much together. However, I don't think our son, or other other youngsters on the trip would have enjoyed it nearly so much had it gone on much past the 3 days. Actually the teenaged girl had already been on a Jane Austen tour with the same company, and she was clearly tired of the coach.
The second time we went to England, we traveled around on our own, using the railway system. It took a lot of planning, but turned out very well. We based ourselves in three main locations and took day trips from there. We were in the UK about 3 weeks, so roughly a week in each place. Trains are easy to use and we found public transport worked well, too. Most of the time, anyway!
So I join the many other voices urging you to plan it yourself. I think you'll have a much better time!