To take benefit of the best prices you will need to prove you are not a business traveller, en route to the 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 grantham station but you may be asked to provide them on your travels from the station to the airport.
Going to the airport on the train is great, you can sleep, read a book (even at night), play travel scrabble, or just gaze out of the window... The other caveat to buying these cheap train tickets from the station to gatwick airport is that there must be at least two adults travelling together. But another great benefit is that children go free. All children under 5 go free, and then one child over five but under sixteen per grown up travelling on the train to the airport.
make sure you leave enough time to get to gatwick airport early enough to eat, shop etc, so check the times of trains from the station before you go. If you end up with spare time at gatwick airport you can always read a book or play travel scrabble again! As you have bought yr ticket in advance, you don't need to worry about the opening times of grantham station.
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