A limited liability partnership (LLP) is a relatively new form of business entity. It's effectively a cross between a company and a partnership; it operates as a partnership but limits the liability of the partners.
An LLP has its own separate legal identity and has to be registered at Companies House. It has the organisational flexibility of a partnership and would have a written partnership agreement detailing how the partnership will work.
In an LLP, partners are also known as 'members'. As a member of an LLP, you and the other members will be free to agree on the relationship between you, as partners do in a partnership. As a separate legal entity, an LLP can continue to exist despite changes in membership.