To take benefit of these prices you will need to prove you are not a business traveller, on the way 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 provide this when you arrive at edgware station but you may be asked to provide them on yr travels from the station to gatwick airport.
Going to gatwick airport by train is great, you can sleep, read a book (even at night), play travel scrabble, or just gaze out of the window... The other restriction to buying these cheap tickets from the station to gatwick 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 kidover 5 but under sixteen per adult travelling by train to gatwick airport.
make sure you leave enough time to get to the airport early enough to eat, shop and so on, so check the times of trains from the station before you go. If you end up with time to kill at the airport you can always read or play travel scrabble again! As you have bought your ticket in advance, you don't need to worry about the opening times of the station.
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