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 give either yr flight details or your holiday booking reference. I don't think you will need to provide this when you arrive at crewe station but you may be asked to provide them on your journey from crewe station to the airport.
Going to heathrow airport on the train is great, you can take a nap, 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 the station to heathrow airport is that there must be at least two grown ups travelling together. But another great advantage is that children go free. All children under 5 go free, and then one child over 5 but under sixteen per adult travelling by train to heathrow 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 crewe 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 yr train ticket in advance, you don't need to worry about the opening times of the station.
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