Here's my Gran's version which I sing occasionally. It's probably pretty close to the orginal as she would have learnt it when it first appeared.

I'll never forget the day that I was born
Twas on a cold and frosty winter's morn
The doctor said I was a funny chap
And then the nurse she laid me on her lap,
She washed me all over I remember
Then after powder puffing me you see
She laid me in a cradle by the fender
In the little shirt me mother made for me.

The first day that I wore me knickerbocks
I did feel funny after wearing frocks
I looked a little picture they all say
But when I went out on the street to play
All the people in the street at me were staring
So in the street I took em off you see
It's a good thing for me that I was wearing
The little.....

The first time I went on me 'olidays
Upon the briny ocean I did gaze,
The water looked so cool I thought I'd go
And have a swim, but in a minute, Oh!
All the girls on the beach were staring
And some were taking pictures I could see
It's a good......