Dundas Slater, with Houdini's arms handcuffed around a pillar by no less than the head of Scotland Yard, Sir William Melville That's the story that is repeated in subsequent biographies (except Silverman), right up to 2006's The Secret Life of Houdini which added even more colorful embellishments.
The 1928 Harold Kellock biography, Houdini His Life Story, took it to the next level with the full blown story of the all-or-nothing bet between Houdini and Alhambra manager C. He even claimed he escaped from a jail cell!
in 1905, he began to tell the story of his Scotland Yard visit as a legit challenge, the very thing this article says he was denied. However, when Houdini returned to the U.S. stories of his European adventures and victories. It should be noted that this story was almost certainly supplied by Houdini himself.