All motoring offences are in contravention of criminal law. (The only exception is that, in those areas where parking control has been transferred from the police and traffic wardens to council officials, parking violations are no longer criminal offences. Elsewhere parking on a double yellow line, for example, remains a criminal offence).
However a standard level CRB check only shows convictions, reprimands, cautions and warnings. It doesn't show fixed penalties. So if you were convicted before a court the information will show on a standard CRB check. If you simply paid a fixed penalty (which is not the same as a conviction) it won't.
An enhanced CRB check can also show information deemed relevant by a Chief Police Officer. That can include almost anything, including unsubstantiated allegations against the subject of the check, or even against someone they live or associate with. So it follows that there might be circumstances where a Chief Police Officer would deem a fixed penalty notice to be relevant and thus worthy of inclusion.
Chris