Disagree. The Guardian has employed identity politics that are very in line with current left-wing politics, but quite at odds with classical liberalism.
One of the key critiques of The Guardian from the UK left is that they are seen as enabling or allowing quite regressive views on some social issues. It's the area where the left is perhaps most negative to them, with it not being unusual to criticise them for allowing e.g. transphobic views, so it's an odd thing to say. They are very much not in line with UK left-wing politics.
Classical liberalism (Bentham, Mill etc.) is (in today's terms) a center-right philosophy.