I’d recommend The Guardian (https://www.theguardian.com/uk) as a decent alternative source to the BBC (and the BBC News’ kowtowing down to the Conservative Party in recent years - likely for fear of cuts to it’s licence fee by them).
I’m just an American, so it’s hard for me to comment on the British press, but I agree about the Guardian. I started reading Glenn Greenwald there (and although he left) I try to never miss anything he writes.
The Guardian’s own investigative journalism is not afraid to go to places where it may find itself in trouble - as you say with Greenwald’s journalism - and a load of Spooks turning up to destroy evidence at its offices!
(I must give The Intercept https://theintercept.com/ more reading time)
Unfortunately, not a lot of UK news media seem to do it’s own investigative journalism anymore - and also shies away from topics like Hillsborough, Orgreave, and of course News International hacking scandal - which the Guardian has led the way on.
I’d also give a mention to The Telegraph - yes, it is right-wing based - but, like The Guardian - it will attack it’s own side when it feels necessary or if it has overstepped the mark (or through gross incompetency).
Also, like The Guardian, the Telegraph also has guest writers from the ‘other side’, along with environmentalists, scientists and liberals - as well as experts in the field (ie, if the subject of an Education Bill comes up they will give column inches to teachers, headmasters - even children - people who may actually know more than the politicians!) giving them a welcome platform to put their views across for consideration.
For us Brits, Channel 4 News (tv) is also worth a mention - impartial and will ask the hard questions, sometimes uncomfortable (as it should be), and not afraid to take on those in power. Far more fearless than the BBC - and doesn’t have to pander to commercial pressures like ITV.
It used to be quite stuffy or aloof - though that has changed in recent years - for the better too 😃
https://www.channel4.com/news/ & https://twitter.com/channel4news