There’s a discussion on HN here (concerning a specific case where a person running 300 forums has decided to close them all) which contains useful information and links to official docs.
AFAICT, 700 thousand monthly active UK users is the threshold for medium. 7 million is the threshold for large.
Note that, I think, some aspects of the law are not sensitive to the size of the service, where others are.
For more, see
(Draft) Illegal content Codes of Practice for user-to-user services (ofcom link)
I think this is a case of the risk to forum owners being low-probability but high-cost. Individual judgement, and perception of risk and attitude to risk will be in play.