I do not recall where I read that the staircase did not have glass panels, but it must have been incorrect.
In QE2, the Authorized Story by Neil Potter and Jack Frost, second edition, 1969, the following is written -
page 140 "Probably the most dramatic of the public rooms is the Double Room, two decks high with the upper deck acting as a balcony linked by a stainless steel spiral staircase, with glass balustrade and red hand rails."