To take advantage of the best prices you will need to prove you are not a business traveller, on the way to newcastle airport, so you will need to give either your flight numbers or your holiday booking reference. I don't think you will need to provide this when you arrive at the station but you may be asked to provide them on your journey from the station to the airport.
Going to the airport by 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 cheap tickets from west-hampstead station to newcastle 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 kidover 5 but under sixteen per adult travelling on the train to the airport.
make sure you leave enough time to get to the airport early enough to eat, shop etc, so check the times of trains from west-hampstead station before you go. If you end up with time to kill at the airport you can always read or play a game again! As you have bought yr ticket in advance, you don't need to fret about the opening times of the station.
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