To take benefit of the best prices you will need to prove you are a leisure traveller, on the way to heathrow airport, so you will need to provide either your flight numbers or your holiday booking reference. I don't think you will need to give this when you arrive at the 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 (even at night), play travel scrabble, or just gaze out of the window... The other restriction to buying these cheap tickets from worthing 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 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 plenty of time to get to the airport early enough to eat, shop and so on, so check the times of trains from worthing station before you go. If you end up with time to kill at heathrow airport you can always read a book or play a game again! As you have bought your train ticket in advance, you don't need to worry about the opening times of the station.
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