Although Hennessy was unable to read or write due to severe dyslexia, he still wrote his own songs such as "Roll Back the Clouds" and "All the Lies That You Told Me".

[5] A renowned songwriter as well as performer, Hennessy wrote several songs that became hits for other singers including Don't Forget your Shovel, made famous by Christy Moore, and All the Lies that You Told Me, recorded by Frances Black.

He also composed the theme tune and incidental music for the BBC TV series "Get Well Soon" written by Ray Galton (of Steptoe & Son fame) and composed and wrote a musical/feature film about his native Ireland, Two Stops to Paradise[6] Hennessy returned to the studio in 2007, one final time to record an album with both Luka Bloom and Christy Moore sharing vocals on one of the tracks.

[7] In 2005, Christy Moore's rendition of Hennessy's "Don't Forget Your Shovel" was referenced in a UK Number One single "The JCB Song" by Nizlopi: "And the engine rattles my bum like berserk.

He was reported to have died from pleural mesothelioma, a rare form of lung cancer, which has been attributed to his younger years spent working on building sites in London where he was exposed to asbestos dust.