NATS is a private company, the only ANSP in Europe which is not run by government. However the skies are owned by the government and NATS operate with the terms of the licence issued by the government.
You forgot to mention that Zee Govt is the largest shareholder w 49% of the shares. Which means that it will appoint most board members and approve any executives.
Do you still maintain that it's a private company, or would you rather admit it's Zee Govt pretending to be a private company run by Politicians.