If you have an early flight out the next morning, staying there makes a lot of sense. You will have time for a leisure breakfast and it's a quick stroll to South Terminal. The Executive Lounge is okay. Not much in the way of snacks, but there were 2 PCs when I was last there in March.

Otherwise, stay in London. Be sure to leave enough time to get to the airport. Factor in the transfer to Victoria and the Gatwick Express (about 35 minutes).

On my last trip, my seatmate told me a harrowing story. He stayed in London and the Gatwick Express train took 50 minutes. For some inexplicable reason, it stopped for 15 or so minutes. He barely made the flight. Don't know if this is a common occurrence.