The BBFC effectively control[ed] what film makers could economically make
No, they control what film makers can legally exhibit. With very few exceptions, it is not lawful in the UK to exhibit in a public cinema (or publish on video tape or disc) any moving picture work which has not been passed by the BBFC. The economic impact of the BBFC is not primarily from its role as a censor, but from its role as the de jure monopoly provider of classification ratings, which allows it to charge extortionate fees for its service.
The fact that something can be published elsewhere does not have any bearing on whether censorship has happened. Your suggestion that it is otherwise would lead to the conclusion that there is no censorship in China, because everything proscribed by the CPC is freely available somewhere outside China.
No, they control what film makers can legally exhibit. With very few exceptions, it is not lawful in the UK to exhibit in a public cinema (or publish on video tape or disc) any moving picture work which has not been passed by the BBFC. The economic impact of the BBFC is not primarily from its role as a censor, but from its role as the de jure monopoly provider of classification ratings, which allows it to charge extortionate fees for its service.
The fact that something can be published elsewhere does not have any bearing on whether censorship has happened. Your suggestion that it is otherwise would lead to the conclusion that there is no censorship in China, because everything proscribed by the CPC is freely available somewhere outside China.