Ultimately though it is all down to affordability and how much of a sacrifice it is to send them private.
I mean if you were a millionaire, you would just send them private because even if the advantage was 1%, you might as well "buy" it for your children.
If it means a degree of personal and family sacrifice - from the no holiday/no new clothes/no car brigade to the more extreme cases of working all hours and re-mortgaging your home - then my answer is a resounding NO.
Not so much because of the merits of the individual school or sector, but because I think that puts too much pressure on the family but most importantly on that child. Any child in any school could fail, not do too well for so many reasons, and if you've sacrificed so much you won't help but resent that child in a terrible way.
I have personal experience of families whose children have done ok but who have put themselves under huge financial pressure and they have served me a very sound lesson in this respect. To a certain degree you ought to always be a little selfish and not sacrifice everything for someone, even your own children.
As I final point, I think we do focus too much on Oxbridge and Russell Group, life doesn't grind to a halt even if your child doesn't get all As or a First from Oxbridge. In the UK there are so many opportunities (still) to do well, yes maybe they won't be off to do Medicine or Law, but there are a huge multitude of other avenues open, even in today's difficult economic climate.