I don't have any special wisdom but I find Mike Ovey's comments quite helpful,
'A Christian explanation could begin with one of the more sensible secular comments. These are "consumer society riots", says Dr Paul Bagguley, who is a sociologist at Leeds. This is very perceptive. It points clearly to the consumerist, acquisitive nature of the looting, and it hints that these are the kind of riots that a consumer society (and let's not forget, that's all of us) has. It hints that this is the kind of riot you expect from members of a consumer society, not from those who refuse to be part of it. That does not allow me to say the looters are totally alien or other, or even "enemies of society" in a straightforward way. The looters are committed to the consumer society. They're "us", not simply "them".'It's worth reading the rest here although I do think he is somewhat patronising about a Christian response which consists of care, concern and presence which he briefly mentions. And prayer doesn't get a mention.
However the subject of consumerism and it's negative effects are going to have to be faced. A book I read a year or so ago called Affluenza is a powerful indictment of a society which glorifies wealth and possessions (eg Chris Evans and his multiple Ferraris) effects such inequalities breeds.
As a Christian I need to grapple with my innate tendency to acquire possessions and the powerful and yet subtle grip that they can have over me. As Jesus said, 'And why worry about a speck in your friend's eye when you have a log in your own?'