A company is defined as a subsidiary of another company, if it’s holding company: 

• holds a majority of the voting rights in it, or
• is a member of it and has the right to appoint or remove a majority of its board of directors, or
• is a member of it and controls alone, pursuant to an agreement with other members, a majority of the voting rights in it,

or if it is a subsidiary of a company that is itself a subsidiary of that other company.

A company is a “wholly-owned subsidiary of another company if it has no members except that other and that other’s wholly-owned subsidiaries or persons acting on behalf of that other or its wholly-owned subsidiaries.

This definition is taken from the Companies Act 2006