Regulating airspace (and any subsequent slot allocations) and/or complying with MATS Part 1 priorities to issue clearances would meet the
En Route licence requirements.
Otherwise the CAA will have to change the rules with Europe, and itself
However, you can't factor in training aircraft for a 0 rate. It is all or nothing and any 'exclusion' or 'inclusion' would have to be done manually by FMP.
But let's not get confused by the 2 'access' issues.
On one hand, the 'environment' is an en route or arrival regulation. It consists of designated airspace or airfields and is automated, using FPL data to populate it's traffic volumes. It is not exclusive, anyone filing an appropriate FPL will figure in the big scheme of things, and get given a slot if regulations are in force.
On the other hand, the airport operator can set access rules (PPR, slots, etc) to its facilities as it sees fit. Whilst ATC can be given information on this and possibly be contracted by the airport authority to 'police' it, it is not for ATC to set the policy or the access rules. That is between the pilot and the airport authority.
You also have to bear in mind the licenced and unlicenced areas of NATS (in terms of the CAA economic
En Route licence to provide ATS). Cardiff provides a service in the licenced arena to traffic on the Airways. In its unlicenced function, it is providing a service on behalf of the airport authority. So, the rules Chilli quotes apply to the Airways under Cardiff Control only. Trainers can plan to fly within them, and are dealt with as other en route traffic (see first paragraph of this post). For traffic which wishes to make an approach, then the airport operator (administered in the air through NATS ATC) can probably say no or set conditions (such as timing) to any operator it wishes with impunity. And I don't think this breaks any 'licence' set by the CAA.