Naval officers had a white cover to be worn at certain times. Naval Uniforms : General Instructions in the Navy List states “White Cap covers. To be worn 1. With white trowsers (sic). 2. With Blue trowsers (a) At Home – From 1st May to 30 Sept inclusive. (b) Abroad – At the discretion of the Senior Naval Officer present.
Current naval caps (all ranks) have white tops as an integral part of the cap.
Army officers had similar white covers for dress caps.
RFC (and so, presumably, Army) officers had a ‘foul weather’ cover for the Service Dress (khaki) cap. These are quite rare, i.e. the IWM uniform curator had never seen one before I showed him the cap which belonged to Humphrey Verdon-Roe (brother of AV Roe) who served as an observer with 100 Squadron.