I have not been able to come up with a prettier looking positive / negative chart, but I think this tells the tale fairly clearly.
First up, note the huge upswing for Livingstone in the London borough of - wait for it, wait for it - Tower Hamlets (and, technically) City and Newham. Quelle surprise. While TH's equivalence to Richard Daley's Chicago for non-traditional democracy is well known, one can also factor in the absence of a Trot mayoral candidate this time. Bar North East, Livingstone did not put as much as 5000 votes anywhere else. What, one wonders did he do to so alienate Merton & Wandsworth? Threaten to cancel Wimbledon and turn Clapham Common into a radioactive tip? He dropped just shy of 10,000 votes from 2008.
Boris gained a small uplift in Barnet & Camden, where Livingstone fell back. I think that certain hateful comments about Jewish Londoners did KL no favours. Boris got his biggest upswing in my own haunt of South West. Set against that, note the heavy falls in the Boris vote in Bexley & Bromley and Havering & Redbridge. I'm putting this down to the bone-idleness of Tories in the eastern outer 'burbs rather than anything else.