I think some people are confusing "closed shop", implying the importance of personal connections, old school tie, special handshakes, or whatever, and "tough industry", implying that people need a lot of luck and/or grafting energy to succeed.
It's incredibly difficult to make a living as musician - arguably harder than making money as a professional writer - but nobody claims there's an old boys' network in the back of the Cavern Club or Royal Albert Hall, do they? It's a just a difficult career choice, and so is comedy/drama/fiction writing. And, no, sense of humour is not sufficient justification for a creer, I'm afraid, any more than musical ability is.
Now, we can argue that the money people, and society in general, don't value creative endeavours enough, and that is probably true; it's a pity maybe that an advertising "creative" gets tens of thousands to essentially nick a concept from an artwork, and plenty of visionary artists earn very little, just as it's a pity that in terms of remuneration it looks as though a banker is considered to be 10 times more valuable than a nurse, but that's a much bigger topic.
As an aside, I am proof that just going to Oxford University doesn't allow you to walk into any old job you fancy (and, yep, I got a good degree, I didn't fail or owt), and certainly doesn't let you wander into the BBC and say "Who wants a script, then lads?". It's a misconception. Now, of course, had I gone to university and spent hundreds of hours working to be a comedy writer from day one, making contacts and whatever, then, yep, my university have been a bit of a help...but that's really no different from putting in hundreds of hours working the stand-up circuit or staging plays or whatever.
As it happens I never joined the Oxford Revue because when I checked them out, they didn't seem very funny to me*. Didn't last time I looked either, and neither did the Oxford Imps improv troupe (although that was a few years ago, which is of course generations in students terms, so it could be brilliant now). Had I had a burning desire to be a professional comedy writer/performer/exec (or, a burning desire for any career whatsoever) I guess I'd have put in the man hours, and might have got a small leg up, but as I didn't...
It's easy to assume that somebody else has had better breaks than you; we all do it, it's natural. But it won't help you achieve anything, and probably isn't very true. If you want to be concerned at inequality, you should worry that a vast number of employers nowadays, especially in the arts, expect people (yep, even Oxbridge grads) to work as interns for a long period without pay to get a forthold in the profession: I see this as a far greater injustice, barring people from jobs due to financial background, rather than whatever ostensibly meritocratic selection process they went through to go to university (or not).
*Pedantic aside: the Oxford Union is nothing to do with writing comedy, or writing anything else. It's a kind of society where people could pay a lot of money to go to a building and...do you, I have no clue what the point of it is, which is why I never joined. There are lectures and stuff. And like, wine tasting. No idea, to be honest.
PS This should be in Writers' Discussion, shouldn't it?
PPS Oh, it's been moved in the time it took me to reply - ninja mods!