EASA has nothing to say about 'Flight Test Bookings', which is merely a sub-section within the Licensing & Training Standards Department of the UK CAA. The only requirement relating to the designation of examiners is ARA.FCL.205(c) which states "The competent authority shall develop procedures to designate examiners for the conduct of skill tests".
There is no EASA requirement (or justification) for the competent authority to get involved in the allocation of examiners for assessments of competence, proficiency checks or any other form of assessment. This is merely another example, among many, of the UK CAA exceeding its remit under EU law either because it is too arrogant or too incompetent to comply.