Botley has associated routeing points Eastleigh and Portsmouth Group, which both seem to be "appropriate" for a journey to London as all three SDS fares Botley, Eastleigh and Portsmouth to London are the same (£35).
Eastleigh to London is valid via Winchester, Basingstoke and then either direct to London via Woking (all on map SW) or via Reading and Slough to Paddington (XR+RG - apparently not from Reading to Waterloo).
Portsmouth Group to London is valid on maps CW+LB, with CW covering the coast to Brighton and LB covering Brighton to London, importantly for you LB includes Brighton to Wivelsfield via Lewes as well as direct.
So you look to be valid either via Botley or via Clapham Junction/London. There's arguments both ways as to whether it'd be valid to go via Botley but not stop there, to be completely safe I'd make sure you're on a train that stops at the point where you switch from using your season on an "outward" to a "return" route or vice versa.