I tell you what , perhaps they may have you on dishonestly filling in the application question if there was one for have you any previous convictions??
I personally would confess to a senior manager , ask them if they are happy with what you do ?? then if they are tell them something has been bothering you ..., Problem is these things in the past have a terrible habit of cropping up through a mate of a mate etc ..better to be honest , a good manager will favour this openess.
I too believe that people should not be judged on what they did when they were younger , we change , get responsabilities and get mature , and even value our freedom , there are others that don't change as well , You are not one of those . best of luck ,