To take advantage of these 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 provide this when you arrive at the station but you may be asked to give them on your travels from the station to the airport.
Going to the airport by train is great, you can sleep, read (even at night), play travel scrabble, or just stare out of the window... The other restriction to buying these cheap train tickets from the station to the 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 sixteen per adult travelling by train to the airport.
make sure you leave plenty of time to get to the airport early enough to eat, shop etc, so check the times of trains from streatham-common station before you go. If you end up with time to kill at the airport you can always read 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.
You can get a train tickets this way from streatham-common station to Gatwick, Luton, Stansted, Manchester, Birmingham, Glasgow, and Newcastle. Holiday Extras don't sell train tickets from streatham-common station to Heathrow and some other airports, because you can't get one ticket to get you all the way there, boo! Damn you Heathrow Express!
Or maybe you meant