Don't even sweat this. I say this as someone who's worked with some proper dodgy characters that somehow had SC.
A chap I used to work with had a pretty shady past and had been to borstel, entered witness protection with name change etc and he didn't have hardly any trouble getting SC (took about 3 months longer than mine), he even worked on the BAE contract at Brough for a while as well when it was granted.