Can I recommend Canford in Dorset? Great drama and music; emphasis on individual as well as team sports; a good charity set up which involves the students going off to India for example to help those less fortunate than themselves; and they produce well rounded individuals. I know, I've been married to one for the past 22 years.
I have to disagree with Xenia; my husband started boarding at 9, at a prep up the road from his home, as he felt he was missing out on the activities by being a day boy. He then went to Canford and to Uni. He did learn discipline and to follow rules, but as he is in the Armed Forces that is useful! He is not scarred at all by the experience, and is a normal, well adjusted, humorous individual with a balanced view of the world.
I would also question you on both working parents being able to leave the children with the Nanny. For the majority of us who work to pay the school fees, and the mortgage, a Nanny is out of the question. I feel that you perhaps live on a higher financial plane than a lot of us, and so you have solutions available to you, that others don't.
Sending a child to board has to be a decision taken by the parents with the input of the child. My brother boarded from 11, as does his eldest son, and the youngest can't wait to go. My son on the other hand, does not wish to board, and so this will not be an issue until he hits sixth form, when I may insist on boarding as a precursor to university.
You also have to take into consideration the circumstances of the families involved. For Service families, boarding can be ideal; the parents can move every two years when the service person is reappointed, and the child gets stability of education and friendships that will last. This is much better than changing school every two years, especially in secondary. Yes I know, you will argue that the parents should weekend. This is not always possible or practical, especially when one is in Cornwall, and the other in Rome or Brussels. Having coped with 2 years of only seeing my husband every six weeks because of the time/distance/ expense equation, I gave up my career; took my son away from his excellent prep, and moved abroad. I would also add the example of a Service man we know whose wife tragically died in her 30s, leaving 2 youngish children. He was sent to sea, and then abroad, and had no option but to send his children to boarding school, where they thrived.
I also have a friend out here whose 12 year old DS has engineered his entrance to Millfield, because the sport is so good, and that is where his interest lies. His mum is none too sure about it, but the lad wants to go and is looking forward to boarding. it's different strokes for different folks, and it always strikes me that as long as the school is carefully selected, and the child understands that they can leave if they wish, then it will work. I went at 16, and had the time of my life...I only wish I'd gone earlier.