Probably not yet, to be honest. But ten London boroughs have taken the plunge and are attempting to interact online with their residents, with varying degrees of success. Some of them are even occasionally interesting, or indeed useful. None of the ten are tweeting prolifically, so don't worry that your council tax is being wasted. Here's a quick summary of how they're doing.
Camden: twitter.com/camdentalking - 178 followers, 193 updates (first tweet February 2009) » Example - "Power cut in the Hampstead Road area, some residents are without electricity: http://bit.ly/qVSL #camdencouncil #eustonroad #camden" » Summary - Started out as a snow update, and still regularly informing residents about changes to services » Also - Flickr
Haringey: twitter.com/LBHaringey - 70 followers, 15 updates (first tweet last week) » Example: "From News Feed: Extra refuse services available for Passover: Special skips will be appearing in .. http://tinyurl.com/d2na7v" » Summary: Very recent; mostly regurgitated newsfeed
Southwark: twitter.com/lb_southwark - 180 followers, 52 updates (first tweet December 2008) » Example:@loobs0 "We'd laid down 500 tonnes of grit between Sunday afternoon and yesterday afternoon. Had another 60 people out gritting last night..." » Summary: Mostly updates on council events and services » Also - Facebook, Flickr, YouTube
Wandsworth: twitter.com/wandbc - 209 followers, 84 updates (first tweet December 2008) » Example: "Dry cleaners go green: Two-thirds of Wandsworth's dry cleaning operators attended a council training workshop on.. http://tinyurl.com/79vxkt..." » Summary: Pure press release sausage factory
If you live elsewhere in the UK, or if you want to discover whether your local councillor is tweeting, check out the ever-growing directory at Cllr Tweeps. It's future of local democracy, you know (or perhaps a pointless micro-audience dead end).