People like Yaxley and other members of CA make up a fringe group of British Society, The New Nationalist Party, a neo-fascist party of the Junta's most hardline defenders, got less than 1% of the vote. For those diehard Junta supporters, it's a mix of nationalism, racism, and dangerous nostalgia, similar to how most people end up in OTL far-right groups. It's most concentrated in the very young (who are too young to remember the dark days of the 70s) or the very old who was insulated from a lot of the chaos.Thanks @powerab for the kind word and response.
I struggle with the notion there would be such a strong pro-Junta sentiment so soon after the restoration of democracy. There does tend to be a "wistful" recollection of such things some years later but the turning of the page would be quite popular.
I'm curious with how the Junta managed to inculcate such a strong aversion to democracy amongst younger people - were newspapers and radio strictly controlled?
Even so, it's not North Korea, nor, I imagine, the German Democratic Republic. Presumably British people were able to travel abroad ? It's hard to isolate Britain from the rest of the world and to be fair you don't suggest Mountbatten or Hill-Norton advocating a form of British Juche.
I'm not sure how the continuing provision of state control in the economy would look especially at a time when the direction of travel elsewhere was so different. Would there still be a British Rail, a British Leyland, a GPO?
What about the cinema? Would American movies be allowed - how does a film like "Saturday Night Fever" resonate to a British audience in mid-70s Junta-run Britain?
What about the arts in general ?
Sport - I could imagine an earlier return of a South African team to England and I imagine Australia and New Zealand would be welcome (that's a thought - how would the Gough Whitlam business develop?) but what about India, Pakistan or the West Indies? Elsewhere, I suspect the top footballers would head to Europe as they did in OTL to some extent - does Hillsborough still happen, presumably Heysel doesn't? What about football hooliganism in general?
There was some form of censorship to films around moral standards under the BBFC and general education was supportive of the Junta but it wasn't on the levels of Juche.
British people were allowed to travel abroad with some monitoring by MI6, with the obvious exceptions of countries like the Soviet Union and Cuba.
Things that the Junta saw as strategically important such as Rail and the Post Office remained in public hands, but companies like Leyland were privatised by Hill-Norton. In fact, communications and post being so centralised was one of the reasons that brought the Junta down. Alan Johnson served as head of the Communications Union and organised a walk-out after Hill-Norton's death. This would completely cripple Britain's communications and snowball into the General Strike of 2003.
British arts are generally much weaker than OTL, many of the big acts of the 60s and 70s like the Beatles emigrated, and new acts were unable to grow in isolated Britain. If you're a European and want to make it in the arts and can't afford to move to LA, you go to Paris, not London.
As for sport, I confess I know very little about sport so I can't really give you an answer, but I encourage wiser people than me to speculate and form a headcanon. I imagine hooliganism would be very political, especially in cities like Liverpool and inner London which had strong Red Brigade presences. I can see the Red Brigades recruiting amongst Liverpool fans. I imagine Hillsborough would still happen leading to increasing amnesty between Merseyside and the Junta.