CSE3120 - How the condition are to be interpreted: Independent Group of Persons: What is a Cost Sharing Group (CSG)?
You should check the other guidance available on GOV.UK from HMRC as Brexit updates to those pages are being prioritised before manuals.
A CSG is an independent group of persons who work together with a common purpose. The CSG is however legally separate from its members. It is established, owned and operated by the members for their cooperative benefit and is independent of any ownership, control or influence outside of the membership. It can be a group of equals or if all the members agree one or more members can have effective control and/or majority ownership of the group. In either case all members must have a legal interest in the CSG. So, for example, if the CSG was established as a limited company all members would have to be shareholders either on an equal basis or if the members agree one or more members could hold more than 50 per cent of the shares. No shares could be held by any person who was not a member of the CSG (see the reference to the case of Toetsing (case C-407/07) in CSE3620).
The CSG does not have to be a limited company, as in the example above. If it is not a limited company ownership and control will take a different form depending on the entity chosen to be the CSG. It can take any form provided it makes supplies in the course or furtherance of a business, see CSE3140.