The USA has a '6 month validity' rule for passports but they also have an agreement with the UK whereby the validity of a British passport is automatically extended for 6 months beyond its nominal expiry date. So, as long as you hold a British passport, you can use it for travel to the USA (subject to visa requirements) as long as you leave the USA on or before the expiry date on the passport:
http://www.usembassy...._visa_niv.html#niv079
You can renew a British passport at any time. Any unexpired period on your old passport (up to a maximum of 9 months) is automatically added to the validity of your new one.
Chris