The Skye Boat Song

"" was a tune that the Second Doctor played on his recorder near the conclusion of the London Event. It was in part a diversion to prevent Colonel Lethbridge-Stewart from overhearing his discussion with Jamie McCrimmon on the Picadilly Circus tube station platform. (TV: The Web of Fear)

Behind the scenes
The work is not identified through dialogue, but simply through a very clear rendition played by Patrick Troughton.