Been playing around on LiveMap with southerly routes from Cockfosters.
Routing down to Shepherds Bush, Fulham and Wandsworth all look OK, returning complete routes with every request.
Balham is where things start to fall apart - more often than not this doesn't return any results, and when it does only the route via the A1 actually reaches Balham, the route via the A406 stops short in Battersea.
Wimbledon, Sutton and Croydon appear completely unreachable... some might consider this to be a beneficial side effect of the routing algorithm.
If I then start looking to the east or west, routes become available again to sought-after destinations such as Knockholt and Chertsey, so unlike some other routing problems we've seen in the past this one doesn't appear to be purely distance related.
Returning to Wimbledon as a destination and tweaking the start point shows that routing from Finchley is reliable, yet no route can be found from the nearby Friern Barnet or Bounds Green. A sanity check shows that Bounds Green to Wandsworth is fine.
Bounds Green to Roehampton is OK, as is Bounds Green to Tibbet's Corner. Attempting the extra mile or so to reach Southfields is a no-no. Oddly, Finchley to Southfields is also a no-no, despite Finchley being valid as a starting point for Wimbledon...