I have been undertaking research into the paper that the poem was typed on. It contained a watermark that had a capital S, then a picture of a crown, then a capital O. It also had under this the word 'absorbent'.
I have discovered that this watermark was on paper used by the British Army in the First World War. At this point in time I have not discovered for sure if the British Army was still using this paper during the Second World War, though after the searching I have done, I believe I can assume they were still using it.
I have discovered that this paper was referred to as the Scrowno paper and was used for much of the British government's security printing. The 'S' and 'O' stood for Stationery Office.
One thing I need to consider is how my grandfather (or whom ever wrote/copied this poem) got this paper, as he was serving in the New Zealand Army at the time. Possibly my grandfather traded for it and/or obtained it while in jail (my grandfather had a habit while at base to drink to much, or go wondering off while on marches, which got him in trouble a bit). The jail was run by the British Army. If my pop obtained the paper while in jail this would have occurred within a period of a couple of months during 1941/1942.
I will keep searching to try and locate when and where this paper was in use and by whom. All this information will help me narrow down when my grandfather could have obtained his copy of / wrote the poem.