There's a lot of confusion over things such as the International Driving Permit and the old insurance "green card," not helped by the fact that the rules change regularly and it's often possible to get two different answers from official sources!
For what it's worth, I don't think the fact that you are living in Britain is of much relevance. It's more a case of whether Italy accepts a U.S. license without the official translation which the IDP provides. A quick trawl on the net seems to suggest that they do require an IDP with an American license, and that some car rental companies will insist upon seeing one anyway.
I can't find anything specific about it on the Italian Embassy website, but it might be worth a quick phone call or an e-mail to ask:
Tel: (202) 612-4400
E-mail: stampa@itwash.org
Website: www.italyemb.org
That's the Italian Embassy in the U.S., of course. I wouldn't even bother trying to ask the Italian Embassy in Britain, as they'll probably not have the correct information to hand (and those with a new-style U.K. license definitely do not need an IDP).