Murdoch, I've had a similar situation last year regarding 3rd party electrical sign-off of a new property extension which had been completed without any certificates.
The Owner had come to sell property and new buyers solicitor had picked up that there was no LABC signoff? I flatly refused to sign-off anybody else's work, so the only way it could get it sorted, was by me discussing this personally with the LABC planning officer who agreed in writing that an EICR from me would be sufficient in lieu of the normal sign -off certificate.
This was not a simple process and if Elecsa find the third party Spark has given a full installation sign off for another person's work, then they will be unhappy - and having conversations (thats what they told me anyway! ).
Hope this feedback is useful.