The lack of CPC in pre-1966 light circuits is something that comes up from time to time and really the answer is a rewire to fix that and of course that the cable must be over 57 years old now. If you want to read up on the industry guidance then the Best Practice Guide #1 (covers this situation when doing a CU change) and #4 (suggests coding as C2 for any class I accessories, and C3 for class II, but that is lenient as the regs only allow that for supervised situations) are worth looking at, available for free here:
Best Practice Guides | Electrical Safety First
Electrical Safety First produces, in association with other industry bodies, a range of Best Practice Guides which provide definitive information and guidance on a range of technical subjects.
www.electricalsafetyfirst.org.uk