Just thought I'd update this thread as I had the same problem and found out how to fix it.
I downloaded and installed the Brigmore Witches DLC, but then once installed I disconnected from the network and loaded up Dishonored. While the DLC appeared in the 'Manage Downloadable Content' section, it wasn't in the 'Missions' tab. I quit the game, reconnected to the network, and restarted the game. It found that I was still using an old version so I downloaded version 1.04, and once the game had loaded it gave me a message that the Brigmore Witches DLC had been found and added to the 'Missions' menu.
So it seems you have to be on at least patch 1.04 of the game (and possibly be connected to the network) before you can start this DLC.