All good suggestions everybody. Walking out of Heathrow is an integral part of the "mission" to me so I'm going to try to avoid getting public transport to the canal. I know it's going to be mostly ugly suburbia and I'm probably being a bit of a masochist but, I've flown over it and driven past it so many times I feel I should at least get out and take a walk around there once in my life.
I haven't decided to go east or west when I get to the Grand Union yet. I grew up in Uxbridge and remember the Swan and Bottle well. My parents used to take me there as a kid when it was a Bernie Inn (or was it Schooner Inn?). This was back in the day when a Bernie or Schooner Inn were the classiest night out in town! So going east to the Swan and Bottle then getting the tube from Uxbridge is an option. If I go west I'll probably head north at Bulls Bridge along the Paddington Arm and see if I can get to Little Venice then take the Heathrow Express back. At 13 miles from Bulls Bridge that might be a bit ambitious though.