I don't know about Weston, but Wikipedia says Bert Lee was born and died in London.

Here's my transcription from the sheet music at The National Library of Australia:

A NOISE ANNOYS AN OYSTER
R. P. Weston and Bert Lee, 1921.

1. I was standing in a fish shop. I'd an hour or two to wait,
For the gentleman that kept the shop was filleting a skate,
So I sang a little chorus just to pass the time away.
Then a big fat oyster growl'd at me and leap'd out of the tray.
He bit a lobster's leg off and the fishman was so wild.
He shouted, "Stop that singing! Didn't you learn as a child?

CHORUS: "A noise annoys an oyster,
But a noisy noise annoys an oyster more.
When the west wind whistles through the whiskers of a shrimp,
The poor old oyster feels a trifle limp.
He'll murder mussels if the seaweed rustles,
Or a cockle croaks a chorus on the shore;
For a noise annoys an oyster,
But a noisy noise annoys an oyster more."

2. I was cross with that young oyster, very, very cross indeed,
So when he'd his shell wide open, being of the bulldog breed,
I scoop'd him out and swallowed him, and said, "Well, there, old thing,
That'll stop you biting lobsters just because I care to sing,"
But when in my interior, he tried to loop the loop.
I shouted to a man near me, "Don't gargle with your soup!

3. It was on a British warship back in nineteen-seventeen,
And our gallant lads beneath them saw a great big submarine.
The captain shouted, "Grab your bombs and drop 'em fore and aft!"
But from below the U-boat quickly wireless telegraph'd:
"We'll willingly surrender. Please don't drop your bombs," they said.
"They'd make a fearful noise and we're upon an oyster bed.