Strictly speaking, he's not a great nephew, although it's confusing when relatives by marriage, etc are included.
As I mentioned before, I am a direct descendant of somebody who married Captain James Cook's wife's sister, but that doesn't make him an ancestor of mine.
My point is that he needs to mention any link in the first place to make his point valid. Of course, it makes for better headlines.
John MacDonald was not related by blood to Attlee. He was a child when Attlee died, so wouldn't have known him that well. His grandmother was Attlee's wife's sister, who married an admiral. There is quite a bit written about this admiral, including a lengthy obituary. I would be amazed, if he had a socialist bone in his body.
I have no idea whether John MacDonald is a 'true' socialist. I have no reason to believe he isn't, but by claiming that he's Attlee's great nephew, presumably to make his case seem more shocking, he's opened up his family background to scrutiny.
Attlee himself came from an upper middle class family and went to public school and Oxford. He had been an officer in WW1. There's nothing wrong with that, which is why I find it hypocritical when people go on about people's backgrounds and seem to think all Labour politicians should have a working class background.