As I understand it at present non-UK ATOs test under their national arrangements and (generally) nominate their own examiners. Does this IN change that?
Examining is separate from the training and nothing to do with where the ATO is located or who is the competent authority for the ATO. Remember the ATO is only approved to deliver training, not testing.
If your medical records are with the UK examining is conducted under UK rules and regulations.
For CPL and IR they will designate based on examiner availability in your area.
The CAA are cracking down on some foreign examiners as the standard obviously hasn't meant their standard.
Be warned - There are schools who will tell you they have UK approved examiners - although true in the past several cannot actually offer this for "some reason" which I believe to be connected to the above.