The Star Chamber was an English court that became unpopular because of the political and religious policies King Charles I used it to enforce, and was "officially abolished" in 1641. In reality, however, the Star Chamber continued as a court for the Society of St George. It punished Society members and dealt with any who were tainted by the Mal'akh. As a result, it became a sort of anti-Mal'akh inquisition.
In 1752, when Faction Paradox signed the Gregorian Compact with Britain, the Star Chamber interpreted their armour as a sign that they were the Mal'akh, and they thereafter began an entirely-pointless crusade against them. This crusade culminated in their failed 1834 attack on the Faction's Eleven-Day Empire, which led to the burning down of Parliament. By that time, the Star Chamber was a physical location within Parliament instead of just a group, and this location was destroyed with Parliament. The Star Chamber's successor organisations never approached its effectiveness, possibly because of intervention by the Great Houses using ghost clusters. (PROSE: The Book of the War)
Around 1782, the Star Chamber was the official head of the Service, composed of a Council of five of its members. Of course, its real heads were much more obscure. (PROSE: The Adventuress of Henrietta Street)
In an alternate timeline created by the Oracle, Alan Turing was the inventor of the Turing Shroud, which served as a schematic of an early computer. He was arrested on charges of sexual deviancy by the Star Chamber, which still existed in the 20th century in that timeline. When the Eighth Doctor confronted them, he learned that they justified their actions by preventing change and the development of advanced technology and weapons that could threaten the world and a decent way of life. The fact that they genuinely believed their philosophy confirmed for the Doctor that they had been manipulated by this timeline's version of Sabbath, who acted as the Oracle's agent. (PROSE: The Domino Effect)