Unincorporated association
You can be constituted as an unincorporated association. All you need to do is draw up and agree a constitution to help your group run smoothly.
Because you don’t plan to be a charity or have limited liability, you don’t need to worry about registering with any external organisations such as the Charity Commission or Companies House.
However, you may find that some funders expect you to have a committee structure. Funding applications will often ask about your management committee, and may need to be signed by the Chair, Treasurer or Secretary. This is because they want to know that there is a stable group of named people who will be responsible and accountable for spending the grant money properly.
Your route so far
Open group? Yes Flat structure with no committee Yes Committee paid? No Want charitable status? No Want to be incorporated? No Want to apply for grant funding? Yes