As it happens, a member of my family did go to New Zealand in 1875, but I think this photo was taken in Chester, England. It is possible that it was this Fireman that emigrated. If this is the case, then none of his living descendants knew he had been a Fireman, so nothing, like a helmet, has been passed down. Pity. Also it would mean that the date of late 1860s or 1870s for the phot fits in with this. So I am now beginning to get an idea of who this might be in the photo. But his occupation was a Millwright, so he must have been a part-time fireman, which I suppose might have been the case.
Thank you everybody for your help. I will now get my New Zealand relatives (recently discovered via RootsWeb!) involved and see what we can come up with as to his identity. I was hoping it was my great grandfather, but it looks as if it might have been his brother (the one who emigrated).