FOIA Section 6

6. Publicly-owned companies. — (1) A company is a “publicly-owned company” for the purposes of section 3(1)(b) if— (a) it is wholly owned by the Crown, or (b) it is wholly owned by any public authority listed in Schedule 1 other than— (i) a government department, or (ii) any authority which is listed only in relation to particular information. (2) For the purposes of this section— (a) a company is wholly owned by the Crown if it has no members except— (i) Ministers of the Crown, government departments or companies wholly owned by the Crown, or (ii) persons acting on behalf of Ministers of the Crown, government departments or companies wholly owned by the Crown, and (b)a company is wholly owned by a public authority other than a government department if it has no members except— (i) that public authority or companies wholly owned by that public authority, or (ii) persons acting on behalf of that public authority or of companies wholly owned by that public authority. (3) In this section— “company” includes any body corporate; “Minister of the Crown” includes a Northern Ireland Minister.
Statutelaw.gov.uk.

This section makes some but not all companies in public ownership subject to the Freedom of Information Act.

The definitions of "wholly owned" here are substantially the same as the definitions of "wholly-owned subsidiary" in the Companies Acts.

Until recently, a company had to have at least two members, so a lot of publicly-owned companies have one share held on behalf of the parent authority by its chief executive or similar.