Like 'Jonathan Strange and Mr. Norrell'? How about Daniel O'Malley's 'The Rook'? Then you should get this book.
The old-timey London setting, with secret magical elements, is reminiscent of the former book, but the tone is much less fussy. The supranatural agency and amnesiac heroine reminded me of the latter.
'The Oversight' is the organization of half-fey agents who are sworn to uphold 'The Law and the Lore,' protecting both magical and mundane elements, mainly by keeping them from each other... However, after a past Disaster, the Oversight is radically reduced, and in quite dire straits. They are desperate for new magical members, and in danger of being overwhelmed in their task by maleficent magical forces.
When a girl who seems to have some ability is delivered into their hands, Sara Falk is eager to accept her into the fold... but there could be a trap awaiting her and her friends.
Nice, rich, complex world-building and a good twisty plot make this long book very enjoyable. It's very clearly the start to a series... not all the questions are answered, or issues resolved... but it's done well enough that rather than aggravating me, I'm eagerly anticipating the next volume. I hope Mr. Fletcher is a quick writer!