To take benefit of these prices you will need to prove you are not a business traveller, en route to the airport, so you will need to give either yr flight numbers or your holiday booking reference. I don't think you will need to give this when you arrive at west-hampstead station but you may be asked to provide them on your journey from west-hampstead station to glasgow-international airport.
Going to glasgow-international 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 train tickets from the station to the airport is that there must be at least two adults travelling together. But another great advantage is that kids go free. All kids under 5 go free, and then one kidover five but under sixteen per adult travelling by train to the airport.
make sure you leave plenty of 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 have time to kill at glasgow-international 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 fret about the opening hours of west-hampstead station.
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