To take benefit of the best prices you will need to prove you are not a business traveller, on the way to the airport, so you will need to provide either yr flight details or yr holiday booking reference. I don't think you will need to provide this when you arrive at the station but you may be asked to provide them on your journey from london-kings-cross station to the airport.
Going to stansted 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 tickets from london-kings-cross station to the airport is that there must be at least two grown ups travelling together. But another great benefit is that children go free. All children under five go free, and then one child over five but under sixteen per grown up travelling on the train to the 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 a book or play travel scrabble again! As you have bought your train ticket in advance, you don't need to worry about the opening hours of london-kings-cross station.
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