As a UK license holder operating in the United States, you will be operating under CEPT Recommendation T/R 61-01.
According to the CEPT regulations(PDF), it explicitly states that:
The CEPT Licence permits utilisation of all frequency bands allocated to the Amateur Service and Amateur Satellite Service and authorised in the country where the amateur station is to be operated.
With a note that:
Special attention should be paid to the difference in frequency allocations to the radio amateur services in the three ITU Regions
According to their FAQ document(MS Word document), this is also the case:
Whose operating privileges should the visitor use?
The operating privileges for the visitor operating under the CEPT Licence are defined by the COUNTRY BEING VISITED, NOT THE PRIVILEGES IN HIS [sic] OWN COUNTRY.
So you have full access to all the US bands, regardless of where you are from. Just make sure to operate according to the US regulations at all times.
(Source for this information: the Operating Abroad page on the RSGB website.)