Criminal Record Office records never did show some motoring offences as 'crimes', which explains why the lawyers could be defending a rapist and know he'd done abh or stolen a bottle of milk in the past but not that he'd done 38 in a 30 zone. ! However, had he been convicted of some really serious motoring offence such as causing death by dangerous driving, that would show up on his 'previous'. All the motoring offences were on DVLA records (and would be found if the current charge was itself a serious motoring offence) .
Presumably, if the CRB check is done to the utmost depth all motoring offences are shown but that depth of enquiry is not normally undertaken.