If you must use the Gatwick Express (FCC is just as fast and better if you're headed to the City or the East End), a useful ticket option is an anytime day single from Gatwick Airport to Boundary Zone 4 (£7.50) and a day travelcard for zones 1-4 (£10 for travel before 0930 and £7.30 thereafter or any time on weekends). It's cheaper than a single (£17.90) in any case, and if you are able to get the £7.30 travelcard option, it is also cheaper than a return (£30.80). Furthermore, it includes unlimited travel for the day on train, tube, and DLR services within London zones 1-4, and on all London red bus services.

This cannot however be purchased online or at vending machines, only at ticket windows. The ticket window is obliged to sell you the combination if you ask for it but is not obliged to offer it proactively.