That 'working people' have the ability and intelligence to enter politics is clear - there have been many examples over the years. I do think it is harder for them though. The problem for many is the matter of needing to make a living between finishing their education and making it in politics. If you don't have political (or media) contacts, your parents can't help out financially, and you don't have access to a trust fund, it's a lot more difficult.
Politics, until you get to Cabinet level, is a risky business - getting voted out and losing your income on a regular basis is a lot easier for those with a financial cushion, particularly in the child-rearing years. Also, being taught to debate, to speak in public, to have the confidence that an Eton/Oxbridge education is a huge advantage, and inevitably those from backgrounds that provide those things will outnumber those who don't.
It's a shame that we don't have a system that better nurtures the minds and ambitions of more of the 'non-elite' or 'working class', but as it stands we don't. I do resent the idea that living in Islington, knowing your way around a wine list or having an Oxbridge degree means that you are out of touch, though. It's just reverse snobbery. It's no more true than the idea that if you just have a few O levels, lived in a council flat and had a baby in your teens you are stupid.
Unfortunately, too many people take notice of accent and things like which school/university someone went to, rather than what they have to say. It's utterly depressing, but it pervades British society.