To take advantage 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 details or your holiday booking reference. I don't think you will need to give this when you arrive at mill-hill-broadway station but you may be asked to provide them on yr travels from mill-hill-broadway station to the airport.
Going to the airport by train is great, you can take a nap, read (even at night), play travel scrabble, or just gaze out of the window... The other restriction to buying these inexpensive train tickets from mill-hill-broadway station to stansted airport is that there must be at least two adults travelling together. But another great advantage is that children go free. All children under 5 go free, and then one kidover 5 but under sixteen per adult travelling by train to stansted airport.
make sure you leave enough time to get to the airport early enough to eat, shop and so on, so check the times of trains from the station before you go. If you end up with spare time at the airport you can always read a book or play a game again! As you have bought your ticket in advance, you don't need to worry about the opening hours of the station.
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