Don't assume bad faith when someone expresses their opinion (see rules). When even Wikipedia describes The Guardian's readership as "generally on the mainstream left of British political opinion" (as I quoted in another comment) there is nothing wrong, disingenuous, or inaccurate in saying that The Guardian is left-wing.
Yes, they are generally over the centre line. They are, however, still firmly centre-left, in that The Guardian has opposed every major push towards even mild social democracy. Most of the UK left would find The Guardian's editorial line well to their right.
You're right, I should have talked about the Overton window more generally. But public usage of terminology is part of moving/spreading the window. It's quite apparent in the US discourse when very moderate politicians like US mainstream democrats are characterized as "radical left-wing extremists". Granted, there's a lot of hyperbolical "fascists" and "nazis" thrown around from the other side.
I find mainstream left of UK to be quite clearly center left. The current Labour government policy could be characterized even as center right.
When the person starts out by describing a mainstream paper as left-wing propaganda, I think its fair to be sceptical about the degree of good faith, no?
