While I haven't bothered with University, I did go to an expensive private school (a step below the likes of Eton) (fees paid by a scholarship), and I have had some links to Oxford University which technically make me an alumnus of an Oxford college and gave me the experience of the university without having studied there (long story). So I'm pretty familiar with the people this article is trying to talk about. For example I have been in the same class as the son of Peter Hitchens, the brother of Christopher who is mentioned as an example in the article, and also the same class as a boy from the Getty family.
Overall, I would say that as a country we value talking and arguing highly as skills, more so than many countries. It definitely becomes more noticeable the higher you climb on the social ladder, but that is generally just because the better educated you are, the more practise you get and the more you learn. It's not that middle/upper class education teaches people these things, it's just that, as with all subjects, private education tends to give people an easier ride.
The idea that at OxBridge it's more about talking than knowing. This was much more true before I was born, a few decades ago. It's certainly what many people who went to those universities in the 50s-70s would say.
"Traditionally, elite Britons then leave education aged 21." That has nothing to do with being "elite", simply that the majority of people who go to university don't study past their BA.
"When Tony Blair hinted that Iraq’s 'weapons of mass destruction' could hit London within 45 minutes, the establishment mostly believed him." Actually a huge number of us didn't believe him, but we blamed it on lies rather than mathematical difficulty. Many of us took to the streets in protest against these lies.
"Educated Americans would often praise Blair for arguing the case better than President Bush could." If you have to draw comparison with GWB to prove that someone is good at arguing a case then you've lost the argument already. I don't know a single working class person who doesn't manage to appear more engaged when speaking than Bush.
"But in general, Britain’s ruling classes are funny speakers." Nonsense. Britain as a whole tends to have a sense of humour, in my experience the upper middle class has less humour than lower classes.
"It was the urge to amuse that recently prompted Cameron to riff on an old TV ad and..." It wasn't the urge to amuse, and anyone who tries to suggest that Cameron, or frankly any of our leading politicians, has a sense of humour, hasn't spent enough time listening to them talk. That was Cameron's attempt to appear hip and youthful.
"Admittedly, ignorance sometimes saves Britain’s rulers from error." How can such a claim be made without given a single example or a single piece of logic to justify it. I don't know if it's a good or a bad point because, without any context, I've no idea what he's even trying to say.