The Star Chamber was an English court composed of common law judges and Privy Councillors which supplemented the common law courts. It became unpopular because of the political and religious policies King Charles I used it to enforce, and was officially abolished in 1641.
Actually, the Star Chamber acted as a court for the Society of St George, long after it officially ended. It punished Society members, and dealt with any who were tainted by the Mal'akh. It became something of an anti-Mal'akh inquisition.
In 1752, Faction Paradox signed the Gregorian Compact with Britain. Although there was really no similarity between the Faction and the Mal'akh, the Faction wore rather scary armour and the Star Chamber couldn't distinguish between different groups with offworld influence. The Chamber decided that the Faction were Mal'akh, and began an entirely-pointless crusade against them. (PROSE: The Adventuress of Henrietta Street)
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)
The Star Chamber's crusade against Faction Paradox 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: Star Chamber)
In an alternative 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. The Chamber was manipulated by that timeline's version of Sabbath, who acted as the Oracle's agent. The Chamber claimed that its actions were justified because they were preventing change and the development of advanced technology and weapons that could threaten the world and a decent way of life. (PROSE: The Domino Effect)