I don't think there are any airfields with rail or bus links direct from London, but most of the airfields near London will have a station which is close enough to get a taxi.
My personal recommendation would be White Waltham, which is where I fly from. It's about £6 by cab from Maidenhead station (which I've done once or twice when the car's been in the garage, or when I've been drinking), and it's just about walking distance, too, if your friend doesn't mind a half-hour walk.
FFF
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