Then he probably gets remembered as a great patriot, and 'Mosleyism'/'Socialist Imperialism' (if he opposes German and Italian fascists I doubt he'll be willing to use the same name as them even if he believes similar things—he called himself a 'socialist imperialist' in OTL, hence my suggestion of that name) gets remembered as a grand patriotic anti-fascist movement. If he does so early enough and the Blackshirts get enough seats in the House of Commons (admittedly a big ask), he might even get a position in Churchill's Cabinet.
What would then shape the future of the Blackshirts would be what stance they take with regard to Labour nationalisations fter the war. They might just end up joining one of the two big parties; they might end up a third party; if they can present themselves as 'like Labour, but patriotic' or 'like the Conservatives, but like ordinary people rather than patricians' and if the party they're rivalling suffer seriously badly (e.g. Labour backing down in an alt-Falklands crisis and thus hugely harming popular opinion of them) then they might, though probably not, even replace one of the two parties.
More likely, I think, is that they would be a grassroots pro-war right-wing movement that never got many, if even any, seats in the House of Commons and faded away after the war. He'd be the sort of wannabe politician that few people have ever heard of.