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@smiff
I did this for fun yesterday on my road bike from Tower Bridge to Kew. I started about 10:30 so there was lots of traffic... Because of rememberance Sunday parliament square was shut so I had skip Lambeth Bridge (just went over and back on Westminster).
I took a wrong turn after Tower Bridge and had to add a loop.
Distance 23.0 mi
Avg Grade -0.0%
Elev Difference -29 ft
Elev Gain 415 ft
Elapsed Time 01:34:40
Resting Time 00:03:56
Average Speed 14.6 mph
http://app.strava.com/activities/27505596
I did it in around 1:35 with a bit of "resting time" (traffic lights) and that was going reasonably quick but not suffering and stopping at traffic lights as I was in club kit. With late night traffic it will definitely be possible to do it quite a bit quicker.