Briefly, the Cottingley Fairies is the name given to a series of photos taken by two young girls in 1917 and 1920 which were greatly publicized with the help of Sir Arthur Conan Doyle, he wrote a book about them called The Coming of the Fairies which claimed they were legit. There is a historical article on the events at wikipedia here. Ironically, Doyle was constantly falling for supernatural claims like these even though he is most famous for creating the logical, evidence-loving Sherlock Holmes. His championing of the pictures eventually did a great deal of damage to his reputation.
Now the correction that needs to be made is in reference to the great Harry Houdini and just a few lines in the script. When the Torchwood team is discussing the history of the photos at the Hub, Owen says that along with Doyle, Houdini also believed they were real. Nothing could be further from the truth. Here PJ Hammond, or whoever wrote the lines in question, is spreading misinformation. I'm not sure where he got this idea of a gullible Houdini from, perhaps from the very inaccurate fictional Hollywood film from 1997 with the dishonest title, FairyTale: A True Story. (Oddly enough Paul McGann had a small role in the film)
Houdini and Doyle were friends but looked at the world in very different ways. Arthur sent Harry some correspondence on the Cottingley Fairies as he did anybody else who cared to listen, but that was it as far as Houdini's interest or involvement was in the obvious hoax. Not wanting to hurt their friendship, Houdini would seldom respond with his true feelings about many of Doyle's beliefs. They eventually would have a falling out when he did just that. Harry Houdini spent the latter part of his life debunking supernatural claims and is a genuine hero of mine so that is why I have a real problem with those few lines of dialogue in the episode.
For those who want to research this subject more, James Randi has written a full account of the hoax in his book Flim-Flam, there is a brief synopsis at his website here. Now all that said, as fiction, the rest of the episode was all in good fun and I even liked the use of the infamous photos in the plot, but my message to the producers is, please try to keep your facts facts and your fiction fiction.