Well,well,well...It is sounding like we are the same family - reading your post, as I know that 11 Stafford Gardens was where Annie lived.
I would much like to see the photo you have of William and family, to see if it is the same as the one I have - the mural style backdrop? Annie (g. grandmother in hat and glasses, William in ww1 uniform). It was indeed 1915, and May on her knee, as Emily Maud died in Jan of 1914. They lived at 48 Enfield Road at that point, and photo likely to be inside that house.
I am May's grandaughter.
Please do get in touch if all of this is sounding likely to you also.