The 'inter-war' John Cooke jnr would have to be a different man; the one I mentioned died in 1900, and 'inter-war' means (in this context) between 1918 and 1939.

For what it's worth, Kilgarriff lists the following songs from him:

Angels Are Hovering Around (words, J S Evalo) 1889
Below! Below!! Below!!! (words, George Horncastle)
Funny Things They Do Upon The Sly (with G W Hunter)
I Want To Meet A Good Young Man (1885)
Married Life (music, G W Hunter)
Millie's Cigar Divan (1885)
So It Was! (words, Horncastle)
What A Blessing (1885)
When The Old Man Came Home Sober