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 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 journey from worthing station to the airport.
Going to heathrow airport on the train is great, you can sleep, read a book (even at night), play travel scrabble, or just stare out of the window... The other caveat to buying these cheap train tickets from the station to the airport is that there must be at least two adults travelling together. But another great advantage is that children go free. All children under 5 go free, and then one child over five but under sixteen per adult travelling on the train to heathrow airport.
make sure you leave enough time to get to heathrow 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 spare time at heathrow airport you can always read a book or play travel scrabble again! As you have bought your ticket in advance, you don't need to worry about the opening times of worthing station.
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