Well, that's the thing about
hidden rooms, they aren't easy to find, and the old BPD weren't the sharpest tools in the shed.
Notice how the storage area off the laundry in the basement has a window? This is the window that is open with a chair under it.
This window opens under the area where the writing pad was situated. There are a few weird 'voids' on this plan, and I draw your attention to an area between the kitchen and the lower hall (also called the butler pantry) and what looks like a closet at one end with another closet in the basement directly below. There was also supposedly a laundry chute that isn't shown. Another void in the basement is directly under the entry on the first floor. This is aside from the 'crawl space' in the basement.
There was also something I can't find at present, about the basement bathroom and a small window directly above on the first floor. It was investigated to see if someone could have climbed up but was dismissed as too small. So I think there may have been an area down there that could have been used to hide something in or even large enough for someone to walk around outside the basement walls but still under the house.