This is a nurse’s uniform hat from the Red Cross from around August 1948. The online guide states: Indoor Uniform: Figure 73 Commando blue seersucker or blue poplin (latest selection since seersucker no longer obtainable) one-piece dress with either long or short sleeves, convertible collar, and 2-inch woven red cross on the upper pocket. Cap: Matching buttoned cap with 1-inch red cross centered on front of facing.
Red Cross Uniform Guide
Online photo of the complete nurses outfit, for reference