AFAIAA, there is no legal requirement other than to comply with Part P of the Building Regs, and that can theoretically be achieved (by a sufficiently skilled and knowledgeable person) without reference to, or compliance with, any Standards or regulations.It may seem daft but you are permitted to wire a house to any EU standard it does not need to be British you could install German "Schuko" CEE 7/4 plug and socket and the LABC has to ensure it is to German standard but as a scheme member British electricians could not fit these sockets they don't comply with British regulations ...
A problem arises because the various certificates and, indeed, an EICR itself, are all BS7671-derived - so an electrician could not really sensibly use those forms/certificates (unless appreciably modified) unless the work (either new or existing) in question had been undertaken to BS7671.
Kind Regards, John