I’d book a later train than some are suggesting
Firstly because your start time is unknown, so if it’s say 11:30 rather than 11:00 that pp was working on, that’s already ‘lost’ you time.
I really hope you have a brilliant run, but there’s always the possibility that you don’t - do your 5 hours might be 5:30, and so you might not be finished until 5ish. Then you need to get medal, bag, take celebratory photos, walk, maybe stretch, start eating. Then get away from the finish area (which will be very crowded, and you have to follow the marshalled routes until you’re well clear)
You could walk for a bit further (north, away from the route and the road closures) then treat yourself to a black cab
Or tube - nearest station which goes directly to KX is Leicester Square, Piccadilly Line - Charing Cross is closest station, but you’d need to change lines. Buses are harder to predict as those which go close to the route may well be on diversion. Sorry to be a pessimist, but if you’ve crocked yourself, you might not feel much like walking, let alone tackling stairs!!
So I’d be planning defensively, expecting everything to take longer than it should. If you get to KX early, there’s loads of places to eat (and sit down) whilst you wait.
I’d go for no earlier than 7pm - because I’d want everything to be as leisurely and unstressed as possible by that stage