A big part of confusion is that the left is no longer interested in the common man and elevating the lower classes. So no, they won't advocate seizing the means. They are instead obsessed with identity politics, which seems to be another aspect of signaling and status seeking. Those who have victim cred wield it, those who don't will display excessive concern to try and be a good ally.
The BBC, like so many others, will absolutely maintain certain narratives from a left Orthodox view, particularly anything to do with sexism, racism or islamophobia.
They decide ahead of time who the victim and oppressor is, and quote only what works to support that hypothesis. There is still a pretense of impartiality, but that's all. There's a reason many classic liberal and alt types have adopted a policy of recording their own interviews and publishing them alongside any outlet featuring them.
It wasn't always so, if you look at articles from their archive of 10+ years ago, you find a much more balanced and neutral perspective.