To take advantage of the best prices you will need to prove you are a leisure traveller, en route to the airport, so you will need to give either your flight numbers or your holiday booking reference. I don't think you will need to provide this when you arrive at finsbury-park station but you may be asked to give them on your journey from finsbury-park station to the airport.
Going to the airport on the train is great, you can take a nap, read (even at night), play a game, or just gaze out of the window... The other caveat to buying these cheap train tickets from finsbury-park 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 child over 5 but under 16 per adult travelling on the train to the airport.
be sure to leave enough time to get to heathrow airport early enough to eat, shop and so on, so check the times of trains from the 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 times of finsbury-park station.
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