The US Consulate says...
Currently, many British citizens traveling on a valid, individual machine readable passport, with a return or onward ticket, and who are staying for less than 90 days, qualify for the Visa Waiver Program. There are conditions, so please review the information concering visa free travel on the American Embassy London Nonimmigrant Visas Services Home Page.
Travelers with a Criminal conviction(s)
Under United States visa law people who have been arrested are not eligible to travel visa free under the Visa Waiver Program(VWP); they are required to apply for visas before traveling. If the arrest resulted in a conviction, the individual may require a special restricted visa in order to travel. The Rehabilitation of Offenders Act does not apply to United States visa law. Therefore, even travelers with a spent conviction are not eligible to travel visa free; they must apply for visas.
http://www.usembassy.org.uk/rctour.html
Hope this helps :)