Originally Posted by
alanR
If you go from Westminster it's better to take the District / Circle Line to either Hammersmith or Barrons Court from where it's a few feet walk to the adjacent platform for the Piccadilly Line to Heathrow.
Normally that'd be a good idea - but the first District line train from Westminster is just a little bit too late to connect at Hammersmith/Barons Court to the
first Piccadilly line train to Heathrow (and there's no earlier connection via Earl's Court available either) -
if the first District is running to time then it should just about connect with the
second Piccadilly line train to LHR at with a minute to spare at Hammersmith/Barons Court (District train arrives at 06:06/06:08, Piccadilly train calls there are 06:07/06:09), but I wouldn't want to count on it!
So if one is aiming for the first Tube into Heathrow from Westminster, go via the Jubilee line and Green Park.
Source -
First and last Tube times on the TfL website.