I was interested to read Steve's comment that the song did originate from Cumbria, and whilst the song is not about counting sheep, it is a number song, and I am still inclined to think the 'rum tum tattelam' does relate to the old counting system, of which there are a number of variations, but, of course, we may never know now.

Here are the lyrics of the song I can remember from the 50s:


Number one, number one,
now my song has just begun,
with an rum tum tattelam owd John Bradelam
Oh what country folk we be.

Number two, number two,
some likes a boot and some likes a shoe.
chorus

Number three, number three,
some like coffee and some likes tea.
chorus

Number four, number four,
some likes a gate and some likes a door.
chorus

Number five, number five,
old folks die when they can't stay alive.
chorus

Number six, number six,
old men use crutches when they can't use sticks.
chorus

Number seven, number seven,
when you die you should go to heaven.
chorus

Number eight, number eight,
some likes a door and some likes a gate,
chorus

Number nine, number nine,
some likes beer and some likes wine,
chorus

Number ten, number ten,
when we get to twelve we'll start again,
chorus

Number eleven, number eleven,
much about the same as number seven,
chorus

Number twelve, number twelve,
if you wants anymore, you mun sing it yourselves
chorus