has both a "CPL(A)" entry and rather surprisingly a "PPL(A)" entry as well -
Brilliant, it is my view then that you may fly subject to the PPL on the licence with a class 2 medical (which includes instructing) but a Class 1 will be required when exercising the CPL privileges.
Your ringing a bell in my head as to when this practice started but I can't recall when nor the reasoning behind it. Perhaps Whopity, BEagle or a number of others will be able to expand on this.