Boswell, from Sunderland, died on Sunday at Hexham General Hospital.
He composed "Little Donkey" 50 years ago - a song which has been sung by countless thousands of school children since.
Recordings of it by Gracie Fields and the Beverley Sisters proved to be hits.
His death came just a week before the planned release of a new album of his songs, including a version of "Little Donkey" by opera singer Graeme Danby.
Boswell at times expressed his surprise that "Little Donkey" had always overshadowed his many other musical compositions and achievements.