The actual types of legal form, which are all mutually exclusive, include:
company (several sub-types, or "descriptions", exist)
registered society (again, several sub-types exist)
charitable incorporated organisation (a "CIO")
limited liability partnership (an "LLP")
miscellaneous bodies corporate set up by statute or charter
UKEIGs (the post-Brexit form of the European Economic Interest Group)
UK Societas (post-Brexit form of a Societas Europaea)
possibly some other exotic things
The list above is fairly comprehensive, but not *yet* exhaustive.
Other statuses that legal bodies may have