To take advantage 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 your flight numbers or your holiday booking reference. I don't think you will need to provide this when you arrive at london-kings-cross station but you may be asked to provide them on yr journey from london-kings-cross station to stansted airport.
Going to the airport on the train is great, you can take a nap, read a book (even at night), play travel scrabble, or just gaze out of the window... The other restriction to buying these cheap train tickets from the station to the airport is that there must be at least two adults travelling together. But another great benefit is that children go free. All children under 5 go free, and then one child over five but under 16 per adult travelling by train to stansted airport.
make sure you leave enough time to get to stansted 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 spare time at the 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 hours of the station.
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