I've come to realise that almost all mainstream media is right wing. The Guardian didn't cover the protests on Downing Street six months ago, when hundreds of thousands gathered, and that was a turning point for me.
Is it the Spectator that properly does it? I know there's that and other magazine, one is right, one left.
The thing is if you see whats happening in the states with the SCROTUS banning certain media outlets for daring to question him, you realise that their media is now 100x more independent than ours is, which has become a collection of mouthpieces which generally just tend to tow the government line and present the right wing ideology of their respective proprietors. .
The Spectator is the right wing magazine, and you have the New Statesman to the left. Private eye is generally a good read although somewhat prone to getting involved in long standing crusades about stuff, and also some of the 'factual' reporting on specialist topics is very biased if you actualy know anything about what they are talking about, in my case 'Piloti' is such a case.