With all due respect MarkRae, that is entirely incorrect.
The question which concerns you on the visa waiver form you get on the plane is as follows
Have you ever been arrested or convicted for a crime involving moral turpitude...........................*it goes on*
If this applies to you, then you will have to tick the yes box and you will be sent home.
Wanting to stay in the USA for less than 90 days and being a british citizen are just 2 of the many criteria you have to meet before travelling to the USA.
Crucially for anyone, it depends what the offence was for. For example, if it was for drugs, then you are not permitted to travel. If it was for, say, drunkenss, then since this is not a crime considered to involve moral turpitude, then you are permitted to travel.
However, it is worth noting that the ondon embassy says that anyone who has even been arrested for ANY crime, at any time must apply for a visa. Although this goes further than the US's requirements.