Hi Andy,
Thanks for the reply. It's a tricky one, isn't it!
I've attached a detail from the back of the photo, a serial number. I don't know if it's relevant, or simply some photographer's admin (there's also a handwritten personal note, which I haven't included because I was worried that this wasn't the correct section of the forum for it; I understand that Roots Chat has a separate section for dating photos and identifying handwriting...?).
And also, family tradition would suggest that he lived or was stationed at or near, or passed through, East Grinstead, Sussex, England, some time during the first half of 1940. I share this fact with trepidation as it may be a red herring. As I said in my original post, I have very little to go on.