I biked in London for almost 2 years (Whitechapel to Farringdon, then Deptford Bridge to Farringdon). What I found helped a lot was to avoid roundabouts as much

I biked in London for almost 2 years (Whitechapel to Farringdon, then Deptford Bridge to Farringdon). What I found helped a lot was to avoid roundabouts as much as possible, and be extra cautious when overtaking on the left near stops. Assume everyone is going to turn left in front of you, 50% of the time you'll be right. ;)