Being at a junction the address has been given as 26 King Street which certainly is more definitive than the Gresham Street address which seems to have fluctuated widely. Pubwiki gives: "in the 1841 census; at 32 Gresham Street in 1869; & at 40 Gresham Street by 1899. The earlier name for Gresham street, before 1845, was Cateaton street or Lad lane. The earlier address is also the Castle Tavern, 12 Cateaton street, Guildhall". Pubwiki lists publicans at the Castle Tavern ,1805 - 1899.
We think there may be confusion with 2 other nearby Castle Taverns, mentioned by British History On-line: "Castle Tavern Court West out of Milk Street with a narrow passage into Wood Street (Strype, ed. 1720, I. iii, 90). So named after the Castle Tavern." This narrow passage may be Compter Passage - a block away to the west.
And the other: "Castle Tavern On the west side of Honey Lane Market and Milk Street, in Cripplegate Ward Within (Strype, 1720 and 1755). No later reference." Honey Lane is actually east of Milk Street.
This is all very puzzling - 3 taverns with the same name so close? Seems unlikely - Perhaps there was just one and the streets have been renamed and renumbered confusing everyone.
And we found nothing to justify the "17th Century" text above the sculpture.
