My understanding is that about 20 years ago it got privatised, with some government oversight. I think that is still the case, it's just now the owner is a foreigner so the tabloids can get worked up.
Also I'm pretty sure this is just the newspapers being sneaky. It was sold off in 2013 under the Conservatives, and now it's being resold to someone else and the media is trying to make it look like Labour are the ones who privatised it.