How many politicians are hired or promoted by prime ministers not because of quality or background but social debts between families? Nobody really tracks those relationships.
Eton isn't regarded as a particularly good school. It is relatively expensive, and preferred by people outside the UK. Their academic results aren't that strong.
And social connections are an aspect of almost every political party. Blair hired almost everyone in Derry Irvine's chambers. Most of the SNP are not only friends, they are actually related to each other. The Tories are possibly the least incestuous because Cameron made a concerted effort to widen the reach of the party in the mid-2000s (this is why the current Cabinet is so diverse).
The reason why there is a concentration of Oxbridge is because, when most of these people went to uni, they were far and away the best. In Scotland, you see the exact same thing with Edinburgh (and strangely, no-one talks about the fact that almost of Sturgeon's clique went to Glasgow...which is, generally, an inferior university). And what you are actually seeing now is that more and more politicians are going to other universities reflecting the fact that non-Oxbridge unis caught up in the 90/00s (and recently, they have dropped off far more...Imperial is ahead in sciences, Oxford PPE is still very good though).
David Cameron - Eton, Philosophy, Politics and Economics at Oxford, went straight into politics.
Theresa May studied Geography at Oxford, worked at Bank of England and a few other institutions for a while.
Boris Johnson - Eton, study of the Classics, ancient literature and classical philosophy. Worked as a journalist, was fired for lying, then became a politician.