I've been out of the training market for a few years but as far as I can remember the aircraft needs the following;
Public transport or aerial work COA.
It needs to be insured for instruction.
You don't need to contact the CAA to tell them you want to train on this machine, the FTO where you are going to do your training needs to inform the CAA that they are using this aircraft for flight training.
Also bare in mind the extra cost of the insurance for flight training, if your only going to fly about 50 -60 hours training on this machine you might not be any better off than just using a machine from the FTO.