To take benefit of these prices you will need to prove you are not a business 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 clacton-on-sea station but you may be asked to give them on your travels from the station to heathrow airport.
Going to the airport on the train is great, you can sleep, read a book (even at night), play a game, or just gaze out of the window... The other restriction to buying these inexpensive train tickets from the station to heathrow airport is that there must be at least two adults travelling together. But another great advantage is that children go free. All children under five go free, and then one kidover five 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 the station before you go. If you have time to kill at the airport you can always read or play a game again! As you have bought yr train ticket in advance, you don't need to fret about the opening hours of the station.
Or maybe you meant