So it's an independent, non-government organisation, but to get a video release you need to have a BBFC classification, and to get that you have to submit your film with a large sum of money?
I believe this is correct.
In which case, isn't it anti competition? I intend to start up my own classification board and charge about 50% of the cost of the BBFC and pinch all of their customers. I'd call it EasyClassification but I'd get sued.
The BBFC became a statutory authority under the Video Recordings Act 1985 (and as amended); to create a competitor would be akin to creating a competitor to a local health authority. It's perfectly possible, but the client - namely, members of the film industry - shan't accept it because it'd go back to pre-BBFC days when there was no coordination in classifying films.
Call it EasyClassification, and you're sure to get sued by Stelios Haji-Ioannou, MD of EasyJet. Not that that should stop you - just hire a good lawyer.