<<Those few who manage to sneak in clearly know someone in the right position...>>
Most definitely not in my case. I did three abroad with IAL, during which time I sat my UK ATC Licence exams and Aerodrome and Approach Ratings. On return to the UK I worked at a small non-State airport. I had my interview for the "Ministry" and was told that I would have to have a medical. I told them that I had only recently had my annual medical and they told me I had passed! They then said I would be joining an adult entry course. I told them that I had a UK Licence which was validated in both ADC and APC. I then had a phone call asking if I would likie to go to Heathrow, which I did, so they sent me on a six week Approach Radar Course. That course was at the same time as the Adult Entry Course and I met the people on it. At least two had UK Licences but had never queried what they had been told.
When I was at Heathrow a number of non-State ATCOs came straight in. If NATS are now turning away such people then that it new policy.