It cannot matter when instructing for the PPL whether you hold a CPL or not. The instructor without a CPL issued will have passed the same written examinations and have completed the same flight Instructor course followed by the same test of competency. The CPL flying course and test is for a different purpose.
The main benefit for me of the CPL is that they will have completed a flying course that offers a much more formalised navigation skill than the PPL. It has always been much clearer to me what I could expect from the CPL/FI for navigation training. Unfortunately the FI course allows for very little time to be given to navigation.
Does anyone know where the CAA list of annotations of privileges, that are entered into the instructors licence, can be found? I would expect to be able to identify the privileges of the FI at a glance.