To take benefit 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 give 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 provide them on yr journey from the station to luton airport.
Going to luton airport on the train is great, you can sleep, read a book (even at night), play travel scrabble, or just gaze out of the window... The other restriction to buying these inexpensive train tickets from wood-green station to the airport is that there must be at least two adults travelling together. But another great advantage is that children go free. All children under five go free, and then one kidover 5 but under sixteen per grown up travelling by train to luton airport.
be sure to leave enough time to get to the airport early enough to eat, shop etc, so check the times of trains from the 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 worry about the opening times of the station.
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