I am sorry but I do not agree. I used to be an administrator at a private children's home for lads 11-17 with emotional and bahvioural difficulties and was responsible for checking CRB checks (enhanced) were in correct company name. I enquired initially if we could take individual CRB checks for prospective employees where they were recently checked by another company and was told by CRB that NO, this was not acceptable as we had to be sure that they were 'clean' the day they started with us. I know it is unlikely but as they said, if anything rears it's head and you have not carried out the check personally within your company, you are liable for the outcomes. It was time consuming but we did actually have one applicant that had two entries on CRB check having only been checked 3 months before. They were therefore not employed, although they were not sex or abuse crimes, but purely that they had not divulged at application that they had what I remember as cautions.
CRB checks show which company/institution has carried out the check.