This is the version I know, I think it's from the musical show:

Attend the tale of Sweeney Todd
His skin was pale and his eye was odd
He shaved the faces of gentlemen
Who never therafter were heard of again

He trod a path that few have trod, did Sweeney Todd
The demon barber of Fleet Street

He kept a shop in London town
Of fancy clients and good renown
And what if none of there souls were saved
They went to their maker impeccably shaved

By Sweeney, by Sweeney Todd
The demon barber of Fleet Street

Swing your razor wide, Sweeney, hold it to the skies
Freely flows the blood of those who moralise

His needs were few, his room was bare
A lavabo and a fancy chair
A mug of suds and a leather strop
An apron, a towel, a pail and a mop

For neatness he deserves a nod, Does Sweeney Todd
The demon barber of Fleet Street

In conspicuous Sweeney was
Quick and quiet and clean 'e was
Back of his smile, under his word
Sweeney heard music that nobody heard

Sweeney pondered and Sweeney planned
Like a perfect machine 'e planned
Sweeney was smooth, Sweeney was subtle
Sweeney would blink and rats would scuttle

Sweeney, Sweeney, Sweeney, Sweeney

Attend the tale of Sweeney Todd
He served a dark and a hungry God
To seek revenge may lead to Hell,
But everyone does it, and seldom as well
As Sweeney, as Sweeney Todd
The demon barber of Fleet.....Street.