The above is the scholarly, historic view. However, when it comes to music publishing, all bets are off. The song title has been variously given as--

COURT OF KING CARACTACUS sung by Rolf Harris on his album "Court of King Caractacus," 1964 (and several subsequent collections); and by The Irish Descendants on "Across the Water," 2004. At least one collection featuring Harris' recording has it as COURT OF KING CARACTICUS.

KING CARACTACUS, sung by Seamus Kennedy on "By Popular Demand."

KING CORACTACUS sung by the Paul O'Brien All Stars Band on "Ultimate Children's Party," 2000. Some collections featuring this band call it KING CORACTICUS.

However, much older than all of them is KING OF KARACTACUS sung by Rich and Rich on "Cockney Kings of Music Hall," Saydisc, 1995.

The British Library Sound Archive confirms this spelling and gives the further information of crediting "Layton" as the author, but I have been unable to find a date for that recording.