Many air traffic systems around the world, including some in the UK, do not show non-squawking aircraft to the controller. This is particularly true for civilian controllers monitoring the upper air, who may only be presented with symbology derived from secondary surveillance systems, not even 'raw' secondary returns.
Thanks for that, I learn again from Pprune. Why would you not want to see non transponding aircraft? Would it just overload the controller?
Can't say I've ever flown in an area where only transponding traffic was shown otherwise I wouldn't get non transponding traffic as conflicts! However, I rarely venture into the oxygen starved areas of the airspace.