"....no Chancellor of the Exchequer came from Eton..."
OK, I did note you also said in the past 40 years but the headline message and the gist of it is misleading, to say the least.
Of course, there had been many OE's who were Chancellors of the Exchequer in the past - at least half-a-dozen or more: Walpole, Grenville, North, Canning, Gladstone, Randolf Churchill and Macmillan, etc. Most of these gentlemen went on to become Prime Minister, of course.
"It looks like you can be groomed to be a PM...but not way you can pull it off if you don't have what it takes to be a Chancellor. Thanks god some things in this world are more than merit than privilege..that tells you the profile a bit.... just saying."
We know what you're insinuating but please be assured privilege alone won't get you everything you want. Boris Johnson didn't exactly get to where he is today just because he's "privileged". He was challenged all the way through last July when Theresa May resigned as PM. And again in December but this time on a national scale in a general election. The Premiership wasn't exactly handed down to him on a silver plate.
Oh, btw, modern Etonians are much smarter than you think - who wants to be 'The Chancellor' when you can be his boss? 
OK, jokes aside, but OP, given your circumstances I think by concentrating more on the Eton King's Scholarship is the best way forward for your child. I've discounted St Paul's because it's not a traditional full boarding boys public school that you want. WinColl is just too inward looking. Only thing I'm worried is that Eton is too competitive when you say your son doesn't like sports which is exactly where one learns to be competitive. This is where all the Boris Johnsons, Duke of Wellingtons, etc learn their trade!
And no, I'm not worried about the academics, bullying, etc at Eton at all. Academics, you just have to refer to the last few years league tables to see where Eton stands; and the bullying? It hardly exist!