Captain Jack Harkness - S1-E12
Factual error: When Gwen finds Toshiko's hidden message from 1941, she realizes that it was written in blood, and her flashlight reveals the bright red letters on the now-yellowed piece of paper. But after 60+ years, the iron in the blood would oxidize. The writing on the note should be rust-brown, not red. (00:33:40)
Answer: He might have requisitioned or stolen it from Torchwood London, or he might have been ready down below once it'd been severed, searching for "the right Doctor" and not knowing that the newly-regenerated Doctor was the one he was looking for.
Captain Defenestrator