I've been singing this one for over 30 years but have no idea of the true origins. I was told it dated from the 1920's but that new verses got added all the time. The reference to cookies rather than biscuits suggests that it is American in origin.

AWAY WITH RUM

CHORUS
Away!Away! With rum, by gum.   With rum by gum, with rum by gum.
Away! Away! With rum by gum,   That's the song of the Salvation Army

We are coming! We are coming our brave little band
On the right side of temperance we come for to stand
We don't smoke tobacco for this we do think,
That the people who do so are liable to drink

Oh! We never eat cookies 'cos cookies have yeast
And a bite from a cookie turns a man to a beast.
Oh! Can you imagine a sorrier sight,
Than a man eating cookies until he gets tight?

Oh! We never eat fruit cake 'cos fruit contains rum,& a bite from a cake turns a man to a bum.
Oh! Can you imagine a sadder disgrace,
Than a man in the gutter with crumbs on his face?

Oh! We never send clothes to be dry cleaned or pressed,
'Cos ether and alcohol are used in the quest.
There's nothing so sorry or sad I suppose,
Than a man getting drunk from the smell of his clothes

Oh! We do not go hiking 'cos it gives you sore feet,   'Tho surgical spirit will cure it a treat.
Because it gets through the skin by osmosis,
And you end up with ten drunk little toeses

Oh! We never use 'Brylcreem' as it's got bay rum,
And too many rubbings turn a fellow quite numb.
And now here's a thought that should have you in fits,
Just imagine those millions of paralytic nits...