There is no such thing as a 'Commercial Flight Instructor'.
To conduct flight instruction for the issue of a CPL(A) a FI(A) must have completed at least 500 hours of flight time as a pilot of aeroplanes including at least 200 hours of flight instruction (and, of course, himself hold a CPL(A)).
There is no difference for holders of an IR, ATP(A) or any other qualification. Standardisation training is up to the individual school as approved by the CAA
Mind you, any school willing to employ an instructor with the minimum qualifications is probably worth avoiding.