From Clapham you can follow the Thames Path down to Wandsworth and pick up the trail from there, might have to dodge a few cars around Wandsworth until you get to King Georges Park and then a few side streets around Earlsfield until you get back on to the river trail proper but then its a good run all the way down to Carshalton and back.
Of course you could always stay on the Thames Path and follow that up river, once pass Putney Bridge its all tow path.
Khanivore - I wouldn't spin your wheels to much about the 10K being slightly short, factors like if you followed the same path as the route was measured, how accurate Garmin's are all play a factor. My Garmin also had this race as just short of 10K.
Not two 10K road races are the same, all have different factors, how hilly, if the race has been measured correctly. Any race offically measured by the British Association of Road Race would/should have their logo on any race documentation, i.e. entry form/web site of which I can't see on anything I've seen for this race.
I would just take comfort that you have set a PB for a10K regardless if it's slightly short or not, the only way you can see if your improving is come back next year and see if you can beat your time! Also if you fancy doing a longer race around the same course then sign up for the Croydon 1/2 Marathon next April. They won't back you run off road plus the MC is much better on that one.
Ah the MC - you mean Co Co don't you? That's Mike Fleet, Chairman of Croydon Harriers, at least I think that his role. Yes does like the sound of this own voice but he means well. Local celebrity? More local "character"