Hi John,
I made the trip to Woking Rail Station last week to play at New Zealand GC, so I can tell you it is about 20-25 minutes from Waterloo. South Kensington to Waterloo by tube involves one easy change and is about 10-12 minutes travel time.
A taxi from Woking station to the course will only be 5 pounds or so. I paid 10 for the trip back up to NZGC at West Byfleet.
Woking is charging 35 pounds after 3.30pm at the moment, which is a steal, I reckon.
The Addington from Sth Kensington is the same 10-12min tube trip to Waterloo, then a 15-20 minute trip from Waterloo East to Croydon and either a 10 quid, 5 minute cab or a 1 pound tram ride of 10 or 15 minutes to Addington Village, which is about 5mins walk to the club. You could also just get the tube from Sth Kensington to Wimbledon and the tram from there to Addington Village. Might be a shade longer, but it will involve fewer changes.
Similarly, to get to Woking, you can get the tube to Wimbledon (which is on the same line as South Kensington) and get the train from there, and in fact that might even be quicker than going to Waterloo.
If you have any other questions, or need me to clarify the rambling mess above, don't hesitate to ask here or by PM.
cheers,
Scott