|Jake Bugg and David Merlini.|
The answer is Jake Bugg, a 20-year-old British singer songwriter, and the song is called "Simple Pleasures" from his second album, Shangri La. The song can also be purchased as a MP3 single on Amazon.
Above is a photo of Bugg with Houdini's technical advisor David Merlini at a recent music festival in Budapest (where the Houdini miniseries was filmed). Keep your ears peeled on Monday and you'll hear Adrien Brody's Houdini give David a namecheck.
Speaking of music from Houdini, John Debney's soundtrack is available now for purchase as digital download. It will be released on two CDs on September 25.
Houdini premieres tomorrow at 9/8c on HISTORY.