To take advantage 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 numbers 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 provide them on your travels from warwick station to the airport.
Going to the airport on the train is great, you can take a nap, read a book (even at night), play travel scrabble, or just stare out of the window... The other restriction to buying these cheap tickets from warwick station to gatwick airport is that there must be at least two grown ups travelling together. But another great benefit is that children go free. All children under five go free, and then one child over 5 but under 16 per grown up travelling by train to the airport.
be sure to leave enough time to get to gatwick airport early enough to eat, shop etc, so check the times of trains from warwick station before you go. If you end up with spare time at the airport you can always read a book or play travel scrabble again! As you have bought your train ticket in advance, you don't need to worry about the opening hours of the station.
Or maybe you meant