From were you turn off near Aldgate East the roads are all pretty big up to and past Tower Bridge so you shouldn't loose much time. You could always go the Greenwhich Foot Tunnel way, Lewisham is a 5-10 min cycle from Greenwhich pier. The first pub on the left as you head away from the foot tunnel on the Greenwich side is really nice as well.
From were you turn off near Aldgate East the roads are all pretty big up to and past Tower Bridge so you shouldn't loose much time. You could always go the Greenwhich Foot Tunnel way, Lewisham is a 5-10 min cycle from Greenwhich pier. The first pub on the left as you head away from the foot tunnel on the Greenwich side is really nice as well.