The Tune is indeed 'Bare Necessities', written by Pat Shaw. The music can be found in the Pat Shaw Collection, book 1.The notes in the book say "Composed in 1974 for Gladys and Joe Muschamp who lived at Bare in Cheshire (UK). They run a hardware shop which Pat suggested should be called 'Bare Necessities', an idea that they readily accepted".
Just thought I'd give credit to the composer :)