Brigadier 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, (PROSE: The Dying Days) his friends and colleagues, such as the Doctor and Sarah Jane Smith, would continue to refer to him as "the Brigadier" (TV: The Poison Sky) or "the Brig" (TV: Revenge of the Slitheen) as he was commonly known. In 2009, Lethbridge-Stewart introduced himself as "Brigadier Sir Alistair Gordon Lethbridge-Stewart". (TV: Enemy of the Bane) A later UNIT leader also held the same rank, Brigadier Winifred Bambera.