If you’re near Tottenham Court Road, the Elizabeth line provides a direct, modern train to Heathrow

https://arthurrops446.wpsuo.com/heathrow-airport-shuttle-and-inter-terminal-transfers-what-s-free-and-when

If you’re near Tottenham Court Road, the Elizabeth line provides a direct, modern train to Heathrow, often faster than the Piccadilly line.