I personally disagree about uni being important for the FCO. I know quite a few people who have got in without an oxbridge education. I agree the better your university, the better your chances, however to claim its only those from oxbridge who get in is in a big big generalisation.
From what I gather of those I know who made it in.
-Ridiculously competitive achievements ie national prizes
-language skills i.e chinese, arabic, swahili ( surprisingly zero EU languages, tho hardly representative of those who make it)
-Extremely articulate
-Passionate travellers
Your uni is immaterial if you can demonstrate those. I've seen the final round 'specimen' information, as long as you are clued up on economics and politics to a very analytical degree and can provide solid analysis of current affairs, you do have a chance.
But I do have to agree, even though the FCO deny this fervently, they do lean towards oxbridge. I find it a real shame that the job market esp for the most competitive come down to alma maters rather than one's education.