DD and I are arriving from USA to Gatwick at 7:30 a.m. on a Tues. morning. We need to be back at Gatwick for a 7:40 p.m. flight to Venice. We want to spend a day walking the Thames Path and going on London Eye and just seeing some sights before getting back to Gatwick. We would like to save a little money and not use Gatwick Express, but we will do so if necessary. We can wait at Gatwick until 9:30 for off-peak hours but when should we leave London for flight to Venice and by what train system, FCC or Southern? Thanks for any advice.