A bit late but...going purely by the JTB set plans, the hole measures out at 2'3" by 2'3" and has a ladder going down.
You can see a crewman exit from it in "Elaan of Troyius" about 10 minutes into the episode, showing that the ladder does indeed extend down to somewhere.
The set for the pilots was built on a soundstage that had an incline and as a result had to be partially built on stilts to keep the floor level (you can see this in the long corridor scenes for WNMHGB, there is a change in level at the far end)
However, by the time the series proper began they had a nice level floor to work with. I'm not sure how they achieved the sub-basement bit, perhaps they literally dug a hole in the floor?