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 yr 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 provide them on your travels from stafford station to the airport.
Going to the airport by train is great, you can take a nap, read (even at night), play a game, or just stare out of the window... The other caveat to buying these cheap tickets from stafford station to stansted 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 5 go free, and then one child over 5 but under sixteen per grown up travelling on the train to stansted airport.
make sure you leave plenty of time to get to the airport early enough to eat, shop and so on, so check the times of trains from stafford 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 fret about the opening hours of stafford station.
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