Dzug's correct. You're not eligible for the visa waiver scheme if you've ever been convicted of an offence. (In fact, you're not eligible if you've ever been arrested even if you weren't charged).
Apply, in plenty of time, for a US visa. Remember that you will have to attend an interview in London and (from the experiences reported by others on this site) the whole interview procedure can take up most of a day. Despite this, I would think that it would be unlikely that you'd be refused a visa.
Chris