The best I can say is yes and no

We know that my mums uncle (GHS Cox)
is in the regimental photo, as it was kept with all his medals and letters, he didn't survive the war and nobody knows which one he is.
Then I got in touch with his sisters grand daughter, she had his sisters old photo's which I promptly scanned. Amongst the collection were maybe two possibilities of a photo of her brother, when I compared the picture's with the regimental picture I couldn't get a positive ID.
So we're non the wiser other than one of them is the spitting image of my uncle Bert

Yes the picture you restored and coloured (so well) is one of the two possibilities, and just to complicate things further ,his sisters husband was also in the middlesex regiment so it could well be him.