An official history is primary evidence for the institution that wrote it

Are official histories primary or secondary sources?

They are primary for the institution's own official view and secondary for events or actors they describe from outside.

Source type depends on the question being asked rather than on a permanent label attached to the book. A British official history is primary evidence when the research subject is the British government's own interpretation or position. It becomes secondary evidence when used to reconstruct what another country or force actually did. The word 'official' does not automatically make a source eyewitness testimony or a definitive account.