In May 2004 I cycled out of Heathrow (Terminal 4) into Cranford, then Hayes, then halfway across the Hayes Bull Bridge a bicycle path will lead you down onto the towpath of the Grand Union Canal. I followed the Grand Union Canal into central London, then took a train from Euston Station to Edinburgh, and rode around Scotland. Returning to the US I spent my last night in the Holland Park hostel, cycled to Hammersmith Station, then cycled on bike paths next to the A315 (I think) to where the A315 crossed a branch of the Grand Union Canal. From there I followed the Grand Union Canal back out to Hayes, got back on the Hayes Bull Bridge, and cycled back to Heathrow/Terminal 4. It's kind of a roundabout way to get into and out of Heathrow/London, but I can't think of a more enjoyable way to recover from a transatlantic flight. You can find my approximate route on Google Earth, the locals are very gracious about giving directions (you probably knew that already), and it would take an effort to get lost once you found the Grand Union Canal.

A few warnings: The Grand Union Canal does split shortly after you leave Hayes, know which branch you want. The local punks (yoofs, as they say) think it's funny to switch the signs. There are barriers to keep motorcycles off the towpath, they are a nuisance to negotiate with a fully loaded touring bike (I know this because...). The path passes under a few bridges where kids will hang out at night, drink, and break the empty bottles on the towpath. No problems in daylight or early evening, but I sliced my front tire open on a broken bottle and cycled 1000 miles around Scotland with a wad of duct tape holding my front tire together.