At the top, it's pretty obvious where to go (one way is blocked by rocks) so go thru the door, which takes you to the Prison Keep. There'll be two sets of passages to either side take the second set of passages, they both go up and either one will do. Get it, then go back out and hang a right and thru that door (the one at the opposite end of the door that let you into the Ministry of Truth). An NPC named 'Grand Inquisitor' is standing next to a desk, and there's a key in that desk.

If memory serves, once you enter at the door next to the woman, you're in a corridor with doors to either side and at the opposite end go thru the right-hand door.