Possibly a not very helpful multi-modal option. It is normally cheaper not to go via London. The Wexham Park to Bracknell bus (53?) and then a Reading Buses 4 to Wokingham station, then the Noth Downs line to Gatwick and change for Hassocks. Depends on how much time you have to waste. Also check service 53 because I believe it doesn't run seven days.
However, in this case possibly not. From Taplow the two fares (both priced by
GWR▸ ) are
£51.40 via London and £57.80 via Reading. From Wokingham not via London (GWR) is
£46.50 (and the any permitted/via London (SW
R) is £59.40, not that it's relevant here). Standard SVR full fare in each case. So it is a bit cheaper, but not enough to make it worthwhile (unless you want to go multimodal for other reasons).