I have no evidence of helmet patches for the 1/3rd Bn., 1/13th Bn., 1/2nd Bn., 1/5th Bn., or 1/16th Bn. There are no other 2" diameter patches held at the IWM which are described as for the helmet cover.
However, I think there is quite good evidence over all three brigades of the 56th Division to suggest that they might have been worn by all the battalions. One very small indication I can see is that the patches for helmet covers are described as "2 inch diameter". There are other 2 inch 'silk' patches held at the IWM from the 1917 Survey, they are just not described as for the helmet cover. I have included these in my illustrations above.
Though it does not say that they are helmet patches, they often come alongside smaller patches of the same type, which are described as worn on the sleeve (often under a shoulder title). This seems to imply, for me, that the larger patch might have some other use.
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