All that can presently (September 2023) be gleaned about Walter King from sheet music covers and by Internet searching is that he was presumably an British music hall performer who has been featured on just one work namely The Marble Arch (1898) music by Bennett Scott, words by C G Cotes and published by Francis, Day & Hunter, London W.C.2, England
There are a few newspaper references from the early 1900's that he was a vocal comedian with a programme of comic songs.
Surfers are welcome to contribute any further information about this performer.