Journeys take between 50 and 60 minutes, depending on boarding location. Passengers in a hurry can catch the Heathrow Express, which operates a non-stop service between London Paddington and the airport in just 15 minutes. The Piccadilly line is the most affordable, the Heathrow Express is the fastest, and the Elizabeth line offers the best all-around value. If you plan to use the Heathrow Express, reserve your tickets well in advance for reduced fares. Heathrow Express - 15 minutes, around £25 a ticket.