I don't believe Kubrick had particular problems with the British Board of Film Censors.
The BBFC never censored A Clockwork Orange, for example. They passed it without cuts, though they had seen a pre-print of the first completed half of the movie as was the custom, and had been concerned that it might not get certification. The censor commended the final movie.
Kubrick personally pulled it from distribution in the UK, after they had passed it and it had a limited release.
https://www.bbfc.co.uk/education/case-studies/clockwork-oran...
The BBFC do not and did not edit films. They are not a government body. They did once call themselves censors (the words of the acronym changed in the 80s), but the point of the BBFC was that the film industry was censoring its own work proactively, and maintaining their own certifications, to avoid government doing it. Similar to what the MPA(A) did.
They still sometimes suggest edits that would keep a film within a particular certification.
In the case of Eyes Wide Shut, it wasn't the BBFC that made any decisions to edit and cut that film; Warner Bros themselves did, based on the US classification they were aiming for.
> Kubrick died within a week of the film release, perhaps he knew too much, perhaps not.
Or perhaps, after a stressful filming, editing and production schedule, a 70 year old man had a heart attack in his sleep.