I can't see anything in CAP 804 that prevents a PPL FI(A) from instructing for the issue of a CPL.
Then you should try looking in the authoritative document
FCL.915 General prerequisites and requirements for instructors
(b) Additional requirements for instructors providing flight instruction in aircraft. An applicant for or the holder of an instructor certificate with privileges to conduct flight instruction in an aircraft shall:
(1) hold at least the licence and, where relevant, the rating for which flight instruction is to be given;