This is a very good reference for the areas affected
Google Map of the Areas affected by the London riots
http://maps.google.co.uk/maps/ms?msid=207192798388318292131.0004aa01af6748773e8f7&msa=0 about 7 years ago
The rioting is widespread but localised.... so there are little pockets of trouble all over the place. But London's a big town, it would be relatively easy to avoid the trouble spots.... just one small problem, new ones pop up out of nowhere. Keep you eyes open to brewing trouble, if you see a gang of youths (especially squaring up to police) go the other way.
This is not a political demonstration, this appears to be opportunism and pure and simple looting, so obviously shopping districts could be targets (especially the ones closest to less well0-off areas). Best thing to do is ask at your hotel/accommodation about which bits of the locale to avoid. about 7 years ago