Well if we are going for real politicians then I shall have to suggest Robert Kilroy-Silk. Did you know he was once a Labour MP? Perhaps he could be Shadow Home Secretary then become Labour leader after John Smith's death in 1994 and continue Kinnock and Smith's work of moving the Party away from doctrinaire socialism. Meanwhile Tony Blair could become a crap TV personality.
David, which Sir Henry Wilson are we talking about here? And Wendall, which Michael Howard? And who is Ward Michael Pakenham?
Saying God could be PM is just silly! Don't you realise he would have to give up his title (Lord God) in order to stand as an MP?
Funny, I thought of posting Churchill and Lennon. Churchill's career in OTL doesn't seem quite real, perhaps it is the result of some Churchill fan writing "If Winston Churchill had gone into Politics"? I don't think Lennon would have had the self-discipline needed to make it to the top job, although I can see him as a rebel Labour MP. But if he goes into politics after becoming famous with the Beatles then I suppose anything could happen.
Daniel O'Connell and Constance Markievicz could be PM of Ireland, but surely not the UK?! I don't see how this could happen.
Tony Hancock might be cool. I picture him as a cynical, witty, self-deprecating "anti-politician". Kind of like Boris Johnson except completely different. I'd vote for him. Did he have political views?
I don't even want to think about a Scargill premiership. I suppose it could happen in a world where the 1980s were a continuation of the worst aspects of the 1970s. Has anyone here read Anthony Burgess's 1985? It's about a nightmarish left-wing Labour government in the 1980s. A Very British Coup by Chris Mullin has the same idea but is much more sympathetic to the left (the PM ends up being deposed in a US backed coup). They are both quite good books. And while I'm recommending books from the 1980s, US/UK by Daphne du Maurier is amusing. That's another one about a US backed coup in the UK. It's scarily plausible.
I would like to see Galloway as PM (in an ATL, not in OTL!). I agree with a lot of what he says and I admire his chutzpah but at the same time I don't trust him (I know he rarely turns up to debates or votes in the House). I went to see him speak once and he is quite charismatic, but charismatic in the same way I imagine Fidel Castro is. Perhaps he could be a British Quisling after the Soviets invade?