According to the Tavistock clinic, a child needs to have had at least three periods before starting blockers as their reproductive system isn't fully formed. Is this true?

No. It is not a requirement in any way shape or form for periods to have started before blockers are given, and this is not suggested in any best practice guidelines for trans healthcare. The risks of psychological trauma caused by allowing menstruation outweighs any of the theoretical benefits posed by the Tavistock.