Depending on your level of nerdness, take the tube to Hatton Cross, and enjoy aeroplanes passing overhead every 90 seconds or so.
https://www.bbc.co.uk/news/uk-england-london-18817472
It's close to the threshold of 27L at Heathrow. I can't recall if/when they swap to 27R when on westerlies. It might be worth finding out.