To take advantage of the best prices you will need to prove you are not a business traveller, en route to the airport, so you will need to give either your flight details or your holiday booking reference. I don't think you will need to give this when you arrive at peckham-rye station but you may be asked to provide them on your travels from the station to gatwick airport.
Going to the airport on the train is great, you can take a nap, read a book (even at night), play a game, or just gaze out of the window... The other caveat to buying these cheap train tickets from the station to the airport is that there must be at least two grown ups travelling together. But another great advantage is that children go free. All children under five go free, and then one child over 5 but under sixteen per adult travelling on the train to the airport.
make sure you leave enough time to get to gatwick airport early enough to eat, shop etc, so check the times of trains from peckham-rye station before you go. If you end up with time to kill at gatwick airport you can always read or play a game again! As you have bought your train ticket in advance, you don't need to worry about the opening times of the station.
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