As I said, I do not think that is really the case with 'Product Standards' (which is what most Standards are). In the case of a Product Standard with which BS7671 requires compliance, I would say that all that is required (or, indeed, all that is possible) is that the manufacturer of the product 'confirms' (i.e. by 'marking', and in the spec) that the product is compliant.BS7671 (as do others) refers to other standards in several places, IMO to fully comply you need to have these standards also (when they apply).
As I said, there's really no point in someone working to BS7671 looking at Product Standards, since there will almost never be any way in which they can confirm for themselves that a product they are using complies with the requirements of that Standard - they have to "take the manufacturers word for it".
As I also said, BS7671 is pretty unusual in being a 'what to do' Standard, rather than a Product one. Indeed, I'm pretty sure that my late father, a Standards Engineer, would have said that it was not 'a Standard' at all, but rather a set of regulations (and would probably draw my attention to the fact that it was subtitled "The IET Wiring Regulations" ).
There may be some Standards with which BS7671 requires compliance which are not Product Standards, but there can't be many, if any.
Kind Regards, John