Well, in his youth Mosley was indeed a member of the Labour Party and regarded as a bit of a rising star. He became disgruntled with the party after the rejection of a policy document he wrote on unemployment and the economy. Some of that is outlined here in my answer to a question about a *Not the Nine O'Clock News' sketch that satirised newspaper obituaries for Mosley.

He also had an eye for branding and publicity, which I mention a bit about here, so the Blair analogy can be seen as relevant in that way. (Mosley's publicity for the BUF had no significant electoral effect, because the party's reputation fell off a cliff after violence at a rally at the Olympia centre in London in 1934.)

Some of the wording of the TVTropes article does sound as if there are far right sympathies at play, e.g. "In popular history he's usually dismissed as a Nazi collaborator".

I don't want to be casting aspersions on the original writer, not having had time to read any where near all of his material - the scenario is in a long forum thread from 2005, with a revised and updated version [here] (https://www.alternatehistory.com/forum/threads/a-greater-britain-mk2.75867/) from 2007, but I don't see that sort of thing being said in the first couple of pages. An idea for a Mosley who remained in the Labour party is interesting. (Its inflection would depends what you do with it and how you write it.) But given the time that it was written, another plausible reading is that it was a way to have a dig at Tony Blair - apparently most of the quotes given to alternate Mosley are real ones from Blair. (In 2005, the far right was not such a major political concern in Britain as they have become, so people might have taken it as given that they wouldn't be assumed to be fellow-travellers with it just by talking about the scenario, and therefore not been at pains to point out they weren't.) I think this should fit as a historiography exemption for discussing the last 20 years...