According to the plan in TTSM vol.2 on page 193, the wheel house contained a signal locker and a flag locker. I expect the signal locker had cubby-holes as Bill mentioned.
The chart table seems to have been in the Navigating Room, not the Chart Room. It's described in the 1935 Olympic auction catalogue as "a mahogany return-end chart chest of eight long drawers, with brass pulls, 13 ft. run, with plate-glass top." As Bill says, these drawers would allow the maps to be stored flat.