The question of why Oxford rather than Cambridge really only begins after the Great War. Prior to this, it was about even between Oxford, Cambridge and everywhere else as to the education of a PM. (I see that there are two metallurgy men amongst the roll of honor.)
So what happened after the Great War that later brought Oxford to the fore as a nursery for budding PMs ? Basically, it was a realization that an education in Classics - hitherto seen as the only true education for anyone - would no longer be adequate in a world beset with industrial scale wars, revolution, mass media, air transport and instant communication via radio/telegraph across the globe. Put on top of that the increasingly complex task of understanding - let alone running - a major economy and its interactions with a global financial system and you soon see the hopelessness of a traditional education centered around Greece and Rome 2,000 years before.
Oxford dons may be vain. But they are never so stupid as to not see a danger to their own importance within UK society and the corridors of power when the world around them (cf. today and the MOOC courses) is changing. They had a confab on what sort of course would be useful and attractive to people running an empire in the 20th century: the result was a sort of "Modern Greats" ("Greats" = Classics) course that combined key elements of philosophy, politics and economics - hence the colloquial name of "PPE" for this course. This was the first "modern world" course of its day and although Cambridge, London and other universities have since then adopted courses along similar lines, none can rival that of Oxford in depth, variety and prestige. Hence the procession of - politically, at least - "ambitious" people to do PPE as a forerunner to a later career in politics, senior civil service, higher professions (useful contacts gained), journalism, diplomatic service - and entertainment !
Have a read through this useful article on Oxford PPE.
That explains why it's Oxford as opposed to anywhere else for the UK's movers and shakers.
Yet there is a question of whether it is a good thing or not to have all the loud souls coming from the same intellectual and moral foundry.