I think this was v common when I was young. Certainly it's what my parents did with my brothers (off to prep at 7/8 after local state). Not with me, but that's another story.
Consequently it was something that I hadn't discounted when I was thinking about my firstborn. We live in an area where everyone with money goes private, to the extent that most of the people I met at postnatal groups didn't even look at local state. We did and it was so much more appealing on every level than the privates we looked at. (OP where are these central london privates with large grounds? The ones we saw didn't even have playgrounds, literally no outside space).
I still had a nagging feeling since I was surrounded by those 'doing their best' by going private. Was I somehow not doing my best? I found it comforting to think that we could always opt for private at 7 or 8 if we so wished. My reasoning was that you can opt out of state to go private, but it was unlikely to happen the other way round.
However, when it got nearer that time, I would no sooner have pulled him out to go to a prep than have sent him off to a seminary. He was happy and thriving and what's more, so were we as a family. I feel so incredibly relieved that we made that choice to go to state school and overall it has made us all happier than we would have been with a horrible commute, financial pressures, lots of homework, boy in one school, girls in another etc.
I also would have felt sort of treacherous if I'd pulled him out. I know others that have done that and, while they're not ostracised, it's hard for them to maintain the links with other families that they enjoyed when they saw them everyday. I know everyone has a right to do as they wish, but you must see that the families you might make friends with might not feel thrilled when you tell them that you're removing your child because 'you have to do the best for them'.
ps none of the (exclusively privately educated) people I grew up with have an inner glow, speak more than one language, are good at debating, can turn tin into gold etc. There are far more bilingual and trilingual kids at my child's state school.