"Dual band" is something of a confusing term, since some American GSM phones can also be dual-band, yet be completely useless in Britain.
The majority of cellphones now sold in the U.K. work on the two British/European bands, which are 900 and 1800MHz. If you look in the instruction book the introductory pages will probably say something like "This phone is suitable for use on the GSM 900 and GSM 1800 systems."
For the U.S., however you need a phone which operates in the 1900MHz band as well. Some American cellular operators are now using the 850 band too, although it's much less common.
Once you have the correct phone, you then need to check that you have an appropriate international roaming agreement with your U.K. cell company, and that the phone is not blocked from international access.
If you call your company's customer serivces number they should be able to tell you about what (if any) roaming agreements apply to your package, as there are numerous variations and they are subject to frequent changes.
Be warned though: Using a cellphone with international roaming can work out very expensive, so check the rates carefully.