From Chichester you can use the 0809 (arr London 1000) and later trains and get a cheap day return at �19.60 via Hassocks/Horsham. (There's also a slightly higher fare which I presume is to Waterloo via Havant)
However, if you are going to use the underground or buses at all, get a 'One day travelcard' at �22.70 for the return trip to London and unlimited travel once you get there. As the standard single cash underground fare is �4 even one journey will leave you in pocket