Here is a Bookfinder.com search with the results pooled. Maybe someone is so interested that they'll buy a copy and take a look at the information in the book to determine authorship.

But wait! I just pulled up a search on the title in Google Books, and the earliest edition I clicked on is 1934 in which the "About this edition" information says

Page count: 32
Published: 1934
Publisher: Francis, Day & Hunter Limited
Language: English
Author: Stanley Holloway
Compiler: Marriott Edgar
Illustrator: John Hassall

The 1949 edition also says "Compiler: Marriott Edgar"

There are copies available in the UK on abebooks.com.

The 1937 book lists the book as Albert, 'Arold and Others, Etc. [Comic Verses.]. publisher as "London" and the author as "Marriott Edgar." It sounds like a reprint or a knockoff.

I hope this helps. Google doesn't offer any images of the books scanned.