John Dee is an agent with British Intelligence.
Since the time frame for Dee's life and covert activities is the second half of the 16th Century during the reign of Elizabeth I of England, there is no government department per se for this. There is just Sir Francis Walsingham, Private Secretary to Her Majesty, and a man who has his tentacles in many areas and where he cannot go, he sends his operatives in his stead. Within the pages of these adventures, that impressive man plays major roles and shows himself to be not only spymaster but also himself an Agent of the Crown.
However, the true star of these tales is John Dee, not Walsingham. The blurbs for the various adventures tell us that through the actions of Dee, "Her Majesty's Secret Service is born with the charismatic John Dee at its head".
According to Wikipedia's entry on John Dee, "John Dee (13 July 1527 - 1608 or 1609) was an English mathematician, astronomer, astrologer, teacher, occultist, and alchemist. He was the court astronomer for, and advisor to, Elizabeth I, and spent much of his time on alchemy, divination, and Hermetic philosophy. As an antiquarian, he had one of the largest libraries in England at the time. As a political advisor, he advocated the foundation of English colonies in the New World to form a "British Empire", a term he is credited with coining."
Since the stories told of him in this series take place starting in 1572, Dee is 45 years old, already well into his careers and a man known throughout both the Royal Court and academia. He is well respected by many, feared by a good number, and hated by a considerable number because to the deeply religious his scientific stance defies the Will of God but to those learned men at universities, his forays into the occult are anathema to their methods.
He makes for a fascinating man to follow.