Ofcom: hopefully, most sites have things in place already for some of it, like a contact point, or a way of trying to take down content.
Discussion
Another question about community-born digital archives, which may have a facility for users to upload content into the archive, which the archive will then display.
Ofcom: start by looking at scope, then about whether it is a "user to user" service (it seems in scope, based on the facts in the question?).
Ofcom has some guidance on file sharing.
But do the risk assessment, and look at how specific measures might apply.
If high risk, there will be different measures.