General Finch was an officer in the British Army. During the dinosaur invasion of London, Finch was placed in charge of British troops who evacuated civilians and maintained order. An extremely arrogant and skeptical man, Finch didn't cooperate well with UNIT, who he thought should worry more about capturing and incarcerating looters than the dinosaurs. Captain Mike Yates served as Finch's UNIT liaison.
In particular, he clashed with Brigadier Lethbridge-Stewart on multiple occasions, insisting that he concentrate only on the looters. When the Doctor and Sarah Jane Smith arrived, after having been mistaken for looters and arrested by Finch's men, the General agreed with their theories about a human agent or agents being responsible for the dinosaurs, but didn't believe time travel was involved. Instead, he said he believed a mad scientist had been cloning them, and they'd escaped from his lab. The Doctor was undaunted, as was Sarah Jane, who believed that a scientist named Professor Whitaker was behind the dinosaurs, citing Whitaker's recent disappearance and his controversial theories about time travel.
Finch and Yates were revealed as members of Operation Golden Age, and he knew very well that Sarah Jane was right about Whitaker. He attempted to kill her, against the wishes of Yates, by locking her inside of a warehouse with a captured tyrannosaurus so she couldn't tell anyone about Whitaker, but she escaped. She didn't know it was Finch who'd locked her in, though, and his involvement went unknown to everyone else. Eventually, though, the General was found out and arrested. He attempted to pull a gun on Sgt. Benton, but Benton attacked him and overpowered him.