Many people enter the USA on the Visa Waiver Program who are not strictly entitled to do so. The US authorities have no direct access to UK judicial records. (Obviously, some information is passed to the US authorities but this would only relate to offences far more serious than yours).
However, it might still be best to do everything 'by the book'. You should be warned, though, that he process takes at least 5 months, during much of which time your passport will be held at the US Embassy in London (effectively prohibiting any international travel during that period).
Full details of the long-winded application process are given in my post, here:
http://www.theanswerbank.co.uk/Travel/Question 289769.html
Chris