Allison, I found the verses in an online "music hall medley" with no credits; the chorus I learned by heart a long time ago. So, I have gone looking (still online) for any way to tie this lyric down. Here's what I find:

Let's All Go To The Music Hall
words: Ralph Butler & Harry Tilsley
music: Horatio Nicholls,
[who is also known as Lawrence Wright]
first copyright 1934, renewed 1961
from the Renewal Registrations,
Library of Congress
Catalog of Copyright Entries
Third Series
Volume 15, Part 5, no. 2
Washington: 1962

Elsewhere it is stated that Bobbie Comber recorded the song.

Not having luck finding the score online though.