Could the Early Morning School have been held in the Wesleyan/Methodist schoolroom on Holliday Street ? Just a suggestion and, if so, the building was still there in the 1950s, so it was probably captured somewhere in photos of the street.
From British History Online:
"Holliday Street mission hall, a brick school chapel, was opened by the Wesleyans in 1875, and cost £1,060. In 1892 sittings were available for 200. Alterations to the building were notified to the Wesleyan Chapel Committee in 1928 and 1933, and in 1940 there was a main hall, seating 150, with three ancillary rooms, of which one was built as a school hall. Church membership in 1932 was 25. The premises were sold in 1955".