By the two addresses with "1" as the house number it seems clear that Irwin's Court was not exactly the same as Irwin's Alley, but it may be that they were associated in some way.
(1785) #1 Irwin's Alley, White, James
(1785) #6 Irwin's Alley, Mathews, Widow
(1785) #7 Irwin's Alley, Brandham, Ebenezer
(1785) #1 Irwin's Court, Vanholt, Valentine