It's taken me 1:15 hrs in a car to drive from New Providence Dock (right next to Canary Wharf) to LHR at 14:00 on a Saturday, using all the usual tricks and avoiding the demonstration in the Westminster area. So on a Friday afternoon, I'd still take the tube (which BTW from Canary Wharf isn't as full as it used to be a year ago ):
1) Take a Stratford train to North Greenwich (one stop).
2) Change platforms.
3) Take a Stanmore train to Waterloo (!).
4) Change to northbound Bakerloo. Do not change at Baker Street - the interchange is easier, but it'll be more difficult to get on.