Brigadier, also called brigadier general, was a military rank on Earth.
The Doctor's good friend and companion, Alistair Gordon Lethbridge-Stewart, was often referred to by this rank. Having first met him as a Colonel, (TV: The Web of Fear) the next time the Second Doctor met Alistair Gordon Lethbridge-Stewart, he had been promoted to Brigadier and made head of the United Kingdom branch of the newly formed UNIT. (TV: The Invasion) Though promoted to General decades later, according to one account, (PROSE: The Dying Days) and attaining the rank of Commander of the Most Excellent Order of the British Empire according to another account, (PROSE: The Two Brigadiers) a different account had Lethbridge-Stewart identify himself to Mrs Wormwood as Brigadier Sir Alistair Gordon Lethbridge-Stewart. (TV: Enemy of the Bane) Following his death, Lethbridge-Stewart's care home nurse called him Brigadier Lethbridge-Stewart, (TV: The Wedding of River Song) while his daughter Kate Stewart knew him as Brigadier Alistair Gordon Lethbridge-Stewart. (TV: The Day of the Doctor)
A later UNIT leader also held the same rank, Brigadier Winifred Bambera. (TV: Battlefield)
In 2000, William Bishop was promoted to Brigadier. (PROSE: The Two Brigadiers)
George Litefoot's father served as a brigadier general in an 1860 expedition to China. (TV: The Talons of Weng-Chiang)
Cutler, the commander of the Snowcap base in Antarctica, held the rank of brigadier general up to when he was killed by Mondasian Cybermen on 1986. (TV: The Tenth Planet)