Yep, purchase off-peak travel card... as previously posted. Also, Lots of attractions and some restaurants in London offer a two for one or 50% discount on production of a train ticket... Don't forget that some musicals / shows don't have a performance on Mondays.
It's a nice walk and orientation from the London eye across to Big ben and Westminster abbey. Consider a walk around Temple....
Consider escaping London for a day... How about Train to the Historic Market Town of Lewes in East Sussex, (1Hr) and on to the Seaside at Brighton (a further 10mins, with direct trains back to London in 50 mins.)