....couldn't HMG sell their holding at any time?..
Well, yes. Thats why PPP is no different to the Privatisation of BT for example. Not too many years after the partial sell-off of BT (nobody mentioned PPP then, just "Privatisation") the government sold of it's Golden share.
There is nothing that I can see to stop them doing the same later / sooner, to NATS.
BEX