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.