Thanks for the replies. I emailed the Criminal Records Bureau and this was their reply.
"This would depend upon the nature of the offence committed and the way in which the points were issued.
If you were convicted by a court then this is would be considered a
conviction and would show up on a CRB check. If you received a fixed
penalty and did not contest it, then it is unlikely that it would be
disclosed on a CRB check."