Major Alex Cosworth was a UNIT officer who served under Brigadier Lethbridge-Stewart. He helped plan the retaking of Stangmoor Prison and the destruction of the Thunderbolt missile, discovering a back entrance in maps of Stangmoor.
His over-familiar nature annoyed the Brigadier. Cosworth would assume the Brigadier was talking to him instead of the men, refer to the planning as similar to making a film, and broke in during the Brigadier's instructions. At one point, he told Lethbridge-Stewart how the man's own plan had "a very good chance of success". The Brigadier sarcastically told him he was relieved to hear that. (TV: The Mind of Evil)
Behind the scenes
Cosworth's first name is only given in the novel The Scales of Injustice.