"I Want a Banana," performed by Arthur Askey and Phil Greenon, appears on the Arthur Askey CD "Hello, Playmates!" ASV CD 5444, 2002.

It also appears spelled "I Wanna Banana" on the various-artists CD "Mairzy Doats: 24 Great Comic Songs," Prism CD 137, 1997.

Yahoo! Shopping > Music has a sound sample, from which I transcribed this:

... really should enjoy.
You can tell the captain. You can tell the crew.
I don't want a monkey or a cockatoo.
I want a banana. I want a banana.
Bring me back a banana, sailor boy.

You brought me back an orange. It gave me great delight.
You brought me back a lemon, and you squeezed me tight....