It is a cap tally with the letters H.M.S. denoting His Majesties' Ship. During WW2 the ship's name did not appear on the tally for security reasons. The lady wearing it is a W.R.E.N. (Women's Royal Naval Service). Or are you referring to the sleeve badge which I have just noticed? It appears to be a propeller with an E below it, which is a Fleet Air Arm badge denoting an Air Mechanic: Engines.
Yes High Wood really sorry I should have been clear that I mean the badge on the sleeve Thank you so much though for the answer that helps me a lot
It looks to be a 2 bladed horizontal air screw with a letter E below that denotes she is an Air Mechanic (E) Engines as described in the second table in this link - The WRNS Steve