The relevant Compliance certificate for DB upgrade is EIC which can be issued by a competent person:
Quoting from IET:
A person carrying out an EICR is required to be competent. The term skilled person (electrically) is used in BS 7671:2018+A1:2020, defined as below:
‘Skilled person (electrically). Person who possesses, as appropriate to the nature of the electrical work to be undertaken, adequate education, training and practical skills, and who is able to perceive risks and avoid hazards that electricity can create.
NOTE 1: The term “(electrically)” is assumed to be present where the term 'skilled person' is used throughout BS 7671.
Many councils will however require EICR from Competent person within a relevant scheme.
While most electricians, whether registered (I am with NAPIT) or not, Me included would NOT issue installation certificate to somebody else's work, It is perfectly common to do condition report on one.
In mine local area we have a REGISTERED electrician who does inspections so fast that tenants sometimes wont notice he was even there (he is rated excellent on trusted trader). So while older installation certificates do give me hints of expected values, their presence or its lack will not influence result of mine inspection by much.