[1]https://en.wikipedia.org/wiki/Public_school_(United_Kingdom)
In recent generations, I have not really noticed that UK as a whole has been particularly innovative relative to its European peers.
It sometimes feel the whole fancy school system in Britain is just a way to maintain an immutable social hierarchy rather than actually making the country more competitive globally.
One might as well put that money in a savings account, move to a country with better public education, then give that money to the kid when they get their first job.
For my mathematics class, about half of my classmates were non-UK citizens. It seems that people are not emigrating away from the UK but they actually immigrating into UK because of the public schools. According to article this type of elite expensive education is only for less than 5% of the population that can afford to pay. Their top public school (Eton College) is virtually impossible to join even if you have tons of money and the prestiges (foreign royalty family).