There are a variety of legal and organisational structures that may suit your business model. Below is a 'bite-size' interpretation; don't be put off by the jargon - just talk with a MKCE professional advisor for more detailed advice.
Unincorporated Association
Has no formal structure, makes its own rules.
Trust
A way of holding assets so as to separate legal ownership from economic interest, with assets owned by trustees.
Companies
A company is owned by its members, who are shareholders if the company is 'limited by shares' or guarantors if it is 'limited by guarantee'. Has good flexibility with internal rules.
Community Interest Company (CIC)
A relatively new structure purpose designed for social enterprises with lock-in of assets to stop the company being sold off for private gain.
Industrial & Provident Societies
An 'IPS' is also a corporate body and its members also benefit from corporate liability. There are two types: a true co-operative society that exclusively serves members interests, and a Community Benefit Society which also serves the wider community.
Charitable Incorporate Organisation (CIO)
Some social enterprises are also charities; there are tax advantages to a charity here, but with regulatory constraints. All activities must be charitable, which means that all profits serve these aims.
Legal structures for Social Enterprises
