The apron literally says “Tate Britain” on it, which is the current name of the original Tate Gallery on Bankside. In the “real world” it didn’t actually get the name Tate Britain until Tate Modern opened in 2000.

The Tate’s other galleries are Tate Liverpool (1988) and Tate St Ives (1993). By “that one in Manchester” do you mean IWM North, which is part of the Imperial War Museum, not the Tate?