First off don't expect the University you go to, to get a foot into the FCO.
It's so competitive now since they opened up their applications, and i'm sure that's the same with the publicly advertised vacancies at MI5/6. But i know two people who were rejected for the FCO, one currently at Durham, and one now teaching English in Italy(nice job methinks!) but who went to Bath and did a French and Russian degree!
I've never felt the atmosphere of an old boys club within the University itself though.