Keith, the BEF codes for divisions didn't go as high as '44'...These appeared with the post-Dunkirk revisions as the security of the earlier series had been compromised.

I have pretty well complete tables of the BEF arm of service markings and most for the Home front during late 1940 / 1941...I suspect that the photo may have been taken at that time. In general, the BEF had either overpainted headlamps (yellow or blue depending on the date) or occasionally a paper mask.

If you mail me a copy of the image, I can see if I can turn up anything. I beleive that you have my e-mail address.