because CPL training can only be carried out on UK registered aircraft.
Where did you get that idea from?
The aircraft can be of any registry. The test aircraft must be approved for the purpose by the CAA or their designated representive ie an Examiner. This form is called an FCL176.
I believe CTC use NZ registered aircraft for their training. They are now on the approved schools for CPL (A) Modular for Bournemouth and NZ.
Approved FTOs