Ministry of Paranormal Affairs

The Ministry of Paranormal Affairs, codenamed Department of Paper Regulations, is a top secret division of the British government. Even most politicians believe it to be either something to do with the publication of academic papers or regulation of paper manufacturing, if they're aware of its existence at all. Only the Prime Minister, the ruling monarch, and individuals within the government with the highest security clearance, know about its full purpose. Similar official bodies exist in most other countries.
The Ministry of Paranormal Affairs, as the name implies, deals with matters relating to magic and its use. Their first priority is always containment: public knowledge of magic is decreed against by the United Nations on the basis of "There are enough threats to global security without having to regulate magic use, which is more unpredictable than the most chaotic of weapons, on a global scale".
That said, in the event that magic does become public knowledge--and there are many in the know who believe it cannot be hidden forever--the Ministry of Paranormal Affairs and similar organisations throughout the world have contingency plans in place, such as detailed laws about magic use ready-drafted, experts who would be appointed as advisors to the politicians in power, information that the public would require prepared for release. Within the Ministry, keeping this plan up to date falls to the Magical Knowledge Exposure Contingency Plan Department (nicknamed within the Ministry as the "Break Glass Department").
Another department within the Ministry deals with cover stories and explanations for freak incidents and unexplainable phenomena known to have a magical component. This can take many forms, from personally assuring a group of scared people that they were hallucinating, to spreading rumours on the internet about much larger incidents to blur the issue. The department in question goes by so many (nick)names (Department of Excuses, Public Relations, Magic Mushrooms Department, Department of Conspiracy Killers, to name a few) that nobody's really sure what it was originally called. Everyone working in and outside the department has their own preference, and occasionally new names for it get coined.
The Ministry employs active agents who work either at a desk or in the field, or both. They are usually seconded from the British security services, or occasionally from outside the establishment altogether and given similar training. Their jobs involve monitoring individuals who use magic, looking out for signs that the knowledge/use of magic is increasing, watching and/or guarding magical places or items to ensure none fall into the wrong hands. From time to time, knowledge of magic will come to someone who proves themselves untrustworthy with it, who then becomes a serious threat to national (or global) security. These agents are tasked with dealing with that kind of situation. The last known instance of this was the individual codenamed Inferno, who had to be incarcerated in a magical prison in the middle of the Atlantic after several times slipping through the Ministry's clutches.
The Ministry also has a Research Department, where magic is studied intensely to better understand it. Obviously any papers published as a result of this research are highly classified, but they make intriguing reading for the handful of people in Britain with the security clearance level to read them.