This version is close to what has been contributed above but in some ways is more complete and does have some significant variation in wording.

I DON'T WANT TO JOIN THE ARMY-2
(Learned from the singing of Denis Puleston of Brookheaven, Long Island)

Monday I touched her on the ankle,
Tuesday I touched her on the knee,
Wednesday with success I lifted up her dress,
Thursday her chemise, gor-blimey!
Friday I put my hand upon it,
Saturday she gave me balls a tweak,
But it was Sunday after supper,
I rammed it up her scupper,
Now I do it seven days a week, gor-blimey!

I don't want to join the Army,
I don't want me knockers shot away,
I just want to hang around,
Piccadilly underground,
Living off the earnings of a high born lady,
Call out the Army and the Navy,
Call out the old Home Guard,
You can always call the loyal Territorials,
They'll save England with a smile, gor-blimey!

Call out me mother and me brother,
Call out the old Home Guard;
You can call out me mother,
Me sister and me brother,
But for God's sake, don't call me!

Then there's always "The Handsome Young Airman" from Card Sandburg's THE AMERICAN SONGBAG, a parody of a much older older song "Wrap Me Up in My Tarpaulin Jacket":

THE HANDSOME YOUNG AIRMAN
(ANON)

A handsome young airman lay dying,
And as on the airdrome he lay,
To mechanics who 'round him came sighing
These parting words he did say:
"Take the cylinders out of my kidneys,
The connecting rods out of my brain,
The crank-shaft out of my backbone,
And assemble the engine again."