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 details or yr 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 give them on yr 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 train tickets from the station to the airport is that there must be at least two grown ups travelling together. But another great benefit is that children go free. All kids under five go free, and then one child over 5 but under 16 per grown up travelling on the train to the airport.
be sure to leave plenty of time to get to glasgow-international 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 your train ticket in advance, you don't need to fret about the opening hours of west-hampstead station.
Or maybe you meant