Was never civvy recognised when I was in. 12 years ago.Air Traffic is not as described as above; but Fighter Controllers are.
ATCO are fully civilian qualified ATCs, who either work in air stations, Swanwick Military ATC or on ships. For the first group, they work either in the tower (like civvies) or in the air station radar room doing closer in control. On ships, their role is analogous, with the added bonus your airfield moves in three dimensions.
JATCC isn't recognised by NATS.
Otherwise, all matelots would leave for higher pay.
I could be wrong though, but that was what the 'score was' when I served. As stated, I could be well out of date.