I'm all for breaking the link between Eton and the cabinet.
However, Oxbridge will always be overrepresented in the government. They do still have the ability to attract the brightest students, and they'll increase this by opening themselves up to state schools. We might well see an increase in the percentage of Oxbridge prime ministers.
We do have to be careful using the word "elitism". Senior government positions are elite positions. We don't want the common man in those positions: I love the guys I have a pint with, but I wouldn't seriously trust them with public office. We want the outstanding, the brilliant, the elite. However, elite should be defined in terms of ability, not social class. Oxbridge has been associated with elitism defined by social class in the past. However, Oxbridge will remain associated with elitism if it truly becomes defined as a meritocracy.