As you will have seen from the admission papers there is a declaration on oath by 6 Freemen that the candidate was born in lawful wedlock. So it would be a question of convincing them. Perhaps this would not be a problem if they were friends of the family; otherwise presumably certificates of baptism and parents' marriage might need to be produced.
Vivienne Aldous, My Ancestors were Freemen of the City of London (1999, p. 58):
"The clerks in the chamberlain's court who made out the papers for city freedom admissions were always careful to record all aspects of qualification by patrimony. Firstly six guarantors, also known as vouchers or compurgators, had to sign the intending freeman's admission paper ... to swear that the person was the legal and natural child of his or her father. This was, in fact, something of a formality, or even a total fiction, for whilst some compurgators were friends or relatives of the intending freeman, the majority were not. It is quite common to find most of the patrimony papers in any given month signed by the same six people, and in these cases it is clear that the compurgators were not necessarily people who had any real link with the intending freeman. Sometimes, the names of the compurgators are those of individuals who are known from other sources to have been staff in the chamberlain's court, or one of the other corporation offices, and so the implication is that they were doing it because they were conveniently close, and probably in order to obtain the small fee payable."
