Can you imagine the rioting that would break out if communications networks were shut down?
Hahaha, I can see it now, furious business people unable to share information about the financial crisis which makes burning London and Birmingham seem as important as nail varnish splattered across a lake of nail varnish remover!
If you "shut down" FB and Twitter (or, God forbid, Mumsnet - cheers for that nightmarish thought, Pandemoniaa!), communication would migrate to other networks, so soon we'd see links as diverse as hotmail and Reuters shut down, as why would you stop, once you started shutting down communications? Then UK-based investors would lose the chance to sell out of any financial markets fall, or buy into any financial markets recovery, and they would, quite rightly bring down the government which decided "to calm things down".
Communication channels are not just used by yobs. It is used by normal people (we are gossiping about the riots, aren't we?), by businesses, by relatives worried about their family members in affected areas.