SirToppam - you are correct that its the first agency capable of doing so verifies a Mode C. The verification can be maintained throughout the next radars/units as long as there is an associated validated Mode A and it has been approved to do so.
As for does it get done at busy airports then yes, always. Departing a/c from say Heathrow that don't say their passing level on first contact will soon realise the stubborn arrogant tone of the controller when they are asked for it and subsequently have futher climb/turns delayed whilst its checked.