I'm at a loss to work out why an eleven year old has to travel from Woking to Surbiton, across fifteen miles of suburbia. It sounds like an education problem, not a public transport problem.
Woking to Kingston actually.
Unfortunately the evidence is that the local comp would not satisfy his potential.
He is very good at maths, and you basically have no chance if you stick just to the (now very basic) Maths A Level syllabus, which most schools will do, since the priority is getting grades, not fulfilling the potential of all http://www.thesundaytimes.co.uk/sto/news/uk_news/Education/article1156765.ece.
The near(ish) private school, which takes a fairly similar profile on entry, Hampton, lays on 24 separate buses, some from 20+ miles away.
Anyway, my point was that A to B even in areas served with fast, regular trains to London is very often a PITA. To get to Reading similarly takes an hour+.