Think this must have been for the Royal Navy, as I think they were the only ones to use 4" guns by 1939. The Textbook of Ammunition 1936 indicates that SAP shells were painted yellow But I think that this had been changed to Middle Buff by 1939. It shows a drawing of a SAP shell with a thin white band just down from the tip, immediately below which is a red band. Around the middle of the shell is a light green band with TROTYL stencilled on in black.
In addition there would have been other info stencilled on the body, indicating the date it was filled, and the place/depot that did the filling, plus lot numbers, and various other info, including the letter N to indicate Naval use. From the groove below where the driving band was it looks like this was for fixed ammunition, so it would not have had the calibre stencilled on it.
Hope this is useful.
Regards,
Roger.