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 your flight numbers or your holiday booking reference. I don't think you will need to give this when you arrive at wood-green station but you may be asked to give them on your journey from wood-green station to the airport.
Going to luton airport on the train is great, you can take a nap, read a book (even at night), play travel scrabble, or just stare out of the window... The other restriction to buying these cheap tickets from the station to luton airport is that there must be at least two adults 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 16 per adult travelling on the train to the airport.
be sure to leave plenty of time to get to luton airport early enough to eat, shop and so on, so check the times of trains from wood-green 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 yr train ticket in advance, you don't need to worry about the opening hours of the station.
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