To say that double or reinforced insulation is not allowed in a domestic installation is incorrect.
Virtually every installation uses double insulation (call it insulated and sheathed if you will) at the origin, i.e. the tails.
Then of course there’s the flexes used in pendants, the double insulated light fittings and extractor fans.
What is not allowed, is an installation which is entirely double insulated.
Certain there have been a number of threads regarding the provision of a CPC at every point and accessory in a wiring system.
As such, I don’t understand why there is any confusion about this?
Yes it is required, except at lampholders having no exposed-conductive parts and suspended from a point which does have a CPC (most people also apply this to other lampholders which are not suspended, such as down lights).
As for the OP, there should either be a CPC present at the light fitting, or at the least, a nearby junction box.
You may find there is sufficient slack in the cable to cut back the outer sheath and still be able to terminate the CPC and live conductors in the new fitting.