Just before I head out to dodge round a few planes......
I remembered a few airproxes where both planes were talking to ATC but still got very close. It was 2 different ATC units and neither new about the other's traffic.
In the Didcot area you have some pilots talking to Farnborough, some to Benson, some to Brize and these days I prefer to talk to Oxford as they are the best in the area. The long and short of it is that you could be talking to one service provider and I could be talking to another but you would not get any warning of my where abouts if your controller did not have a radar that sees my glider mode "S" transponder.
There is a culture in aviation that wrongly assumes that talking to ATC keeps one safe, user beware. Not all ATC units have radar and not all radars see everything at low level.
bb