Comment by pieds
The UK certainly have had its own counterculture. In some ways more than the US. That still doesn't take away from the franchises being published (and in parts made) by US companies with US culture in them.
The UK had an influence in punk music. But it was also banned by the BBC and bands were at times left to tour elsewhere. Japanese companies created most of the affordable electronic instruments. Yet, electronic music in jungle, drum and bass, UK garage and rave culture took off in the UK with influences from reggae, soul and R&B. Now with the help of BBC Radio 1. This style of music then made it into Japanese video games. With similar things happening in the US with jazz, hiphop and house music.
I'm sure it is possible to gotcha the argument. Hollywood has still created far more interpretations of science fiction in media than anyone else. If you really want to argue for British dystopian science fiction movies then Children of Men is an excellent example. But it is also almost the only one of note.
A country with major influence on science fiction that often goes uncredited probably isn't Japan but Canada.
> UK garage and rave culture took off in the UK with influences from reggae, soul and R&B. Now with the help of BBC Radio 1
I think there's an important middle step here, which is stuff that wasn't "banned" but was nevertheless not on the playlist, and the pirate radio stations whose personnel gradually went mainstream. Both from the Radio Caroline era (Jonnie Walker, rock) and Kiss FM (Trevor Nelson, UK garage). Let's not forget the government's attempts to ban the rave scene.
In comics you had 2000AD and Judge Dredd, inspired by the French Metal Hurlant.
> If you really want to argue for British dystopian science fiction movies
Not movies, but TV: Doctor Who (often dystopian), Blake's 7, the Prisoner, and the little-seen but extremely prescient Doomwatch. And of course the darkest nuclear apocalypse movie, Threads. Filmed in the parts of Thatcher-era Sheffield which looked like they had already been nuked.
UK always simply had less money and a narrower set of TV/radio gatekeepers. The diversity and inventiveness is there nonetheless. So, yes, a lot of things have to get American money and licenses in order to be made.