The Underground route to Heathrow is dependant on where you start, also if you have bags or not as some of the stairs up and over track can be wearing. We honed our journey down to this route taking various factors into account.
We always travelled from the east of London, arriving in Liverpool Street main line station. From there either the Circle Line or Hammersmith & City tube to Hammersmith. Out of the station, across the road and within 40 yards into the other section of Hammersmith station. From there the Piccadilly Line directly to Heathrow. From the east we found this by far the most convenient with a single easy change after Liverpool Street, although still plenty of stairs in Liverpool Street station.
As an aside if you have to go out of your way to catch the express trains to Heathrow I can't see the point. In fact you have to be really pressed for time to wish to pay much more to save 30 minutes.
We always travelled from the east of London, arriving in Liverpool Street main line station. From there either the Circle Line or Hammersmith & City tube to Hammersmith. Out of the station, across the road and within 40 yards into the other section of Hammersmith station. From there the Piccadilly Line directly to Heathrow. From the east we found this by far the most convenient with a single easy change after Liverpool Street, although still plenty of stairs in Liverpool Street station.
As an aside if you have to go out of your way to catch the express trains to Heathrow I can't see the point. In fact you have to be really pressed for time to wish to pay much more to save 30 minutes.