To take benefit of these prices you will need to prove you are not a business traveller, en route to stansted airport, so you will need to give either yr flight details or yr holiday booking reference. I don't think you will need to give this when you arrive at vauxhall station but you may be asked to give them on yr travels from vauxhall station to stansted airport.
Going to stansted airport on the train is great, you can sleep, read (even at night), play a game, or just gaze out of the window... The other restriction to buying these cheap tickets from vauxhall station to stansted airport is that there must be at least two grown ups travelling together. But another great benefit is that kids go free. All kids under 5 go free, and then one kidover 5 but under 16 per adult travelling on the train to stansted airport.
be sure to leave plenty of time to get to stansted airport early enough to eat, shop etc, so check the times of trains from vauxhall station before you go. If you have spare time at stansted airport you can always read or play a game again! As you have bought yr ticket in advance, you don't need to worry about the opening times of vauxhall station.
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