Much as I hate to be contentious with the originally quoted date of 1900, the notes of the Central Post Office state that it was built in 1910, yet it was in the photo, with the wall mounted clock on the left of shot?.....
"Sheffield's Head Post Office operated in the square for almost ninety years. Built in 1910 as an addition to the 1897 post office building on Flat Street, it closed in 1999, with the main post office moving to new premises within the Co-op store on Angel Street."
So, I tend to agree with you, madannie77