To take benefit of the best prices you will need to prove you are a leisure traveller, on the way to the airport, so you will need to provide either yr flight details or your holiday booking reference. I don't think you will need to give this when you arrive at the station but you may be asked to give them on your travels from peterborough station to the airport.
Going to the airport on the train is great, you can sleep, 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 the station to the airport is that there must be at least two grown ups travelling together. But another great advantage is that kids go free. All children under 5 go free, and then one child over 5 but under sixteen per adult travelling on the train to luton airport.
be sure to leave plenty of time to get to luton airport early enough to eat, shop etc, so check the times of trains from the station before you go. If you have time to kill 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 fret about the opening times of the station.
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