So, starting at Heathrow T4, head round to T123, back to T5, and then head out to Acton Town.
From there, head one stop to Chiswick Park, then double back and head up to Ealing Broadway..
Head east to West Acton, then walk/trot up to North Ealing on Foot...
The a nice long run up to Uxbridge, double back to Ickenham... From there, again on foot to West Ruislip.. Then from there, one of the longest runs of the day - from West Ruislip to Liverpool Street..
Change lines and head back west to Baker Street..
Then Jubilee Line up to  Wembley Park.. From there take the Met Line to West Harrow, then on foot to North Harrow... Trek up to end of line at Amersham, back to Chalfont and Latimer to do the Chesham branch.. Then back to Moor Park to do the Watford Branch..

To be continued...