No I disagree. As far as my meagre knowledge goes, the number associated with the CE mark is that of the notifed body that assures conformity of the specific device (and by implication the manufacturers design/manufacturing/production, etc, processes surrounding it) when that approach is applicable (according to risk classification of the device). There are other approaches that verify quality systems involved with manufacturing equipment or allow the manufacturer to declare conformity - hence there's not necessarily a number associated with the CE nor type testing involved in all cases.
You are talking about the CE certificate number such as that issued by BSI for Production Quality Assurance, for example, I think (by the way it's a 5-digit code), Kawasaki. Incidentally Therapy equipment has this for its products as far as I'm aware. The number associated with the CE mark on the equipment is actually the notified body number. So the question is which British Standard does the Therapy Equipment fail to meet?