Attached is the well known button for the Women's Legion.
The Imperial War Museum has a different design in its collection:
http://www.iwm.org.uk/collections/item/object/30077000
I copied it and turned it 180 degrees. See attached picture.
The letters are W.S.W.L.
the IWM assumes the letters may be Women's Services.
My guess is War Services Women's Legion.
Does anyone know what these letters are?