Why would it need to be that different? Replace “the Company” with “the Association” and you’d have a decent first pass…
As regards liability, well… someone is still responsible for the site, security, and making sure that relevant data protection legislation, etc are being followed.
Pulled from the UK government page that you linked:
Individual members are personally responsible for any debts and contractual obligations.
I am not a lawyer, but this sounds like members of the association could be held personally responsible in case of a failure there. You may want to get more local legal help, but having a clearly defined chain of responsibility explicitly stated in the TOS sounds like a good idea to me.
Question to ask yourself: is every user of the site a member of the association? If not, you almost certainly have a contact (are implied contacts a thing in the UK?) between “the Association” and regular users.