I am basically in the same situation to you, or was last yr… graduate, single, mountain biker, working in Farringdon (just near St. Pauls).
I would suggest Wandsworth and surounding area as it has the cheapest council tax in the country (correct me if im wrong) or maybe the cheapest in London, so something to think about. Means you are very close to Clapham Junction for trains which is perfect for commute down to Surrey/South Downs/Bracknell etc… Means you have a decent cycle to work to keep fit on the road bike.