Thanks Michelle
I eventually went for the "The Cruel Mother" : Child no. 20 (Version F) although the 'Edinburgh' chorus also appears in Child 10.

Cruel Mother

It fell upon a simmer's day,
   Edinburgh, Edinburgh
It fell upon a simmer's day,
   Stirling for aye
It fell upon a simmer's day
The clerk and lady went to play.
And bonny Saint Johnston stands
fair upon Tay

'If my baby be a son,
I'll make him a lord of high renown.'

She's lean'd her baclc to the waa,
Pray'd that her pains might fa'.

She's lean'd her back to the thorn,
There was her baby born.

'O bonny baby, if ye suck sair,
You'll never suck by my side mair.'

She's riven the muslin frae her head,
Tied the baby hand and feet.

Out she took her little pen knife
Twind the young thing o' its sweet life

She's howked a hole anent the mean
There she laid her sweet baby in

She had her to her father's ha'
She was the meekest maid amang them a'

It fell ance upon a day
She saw twa babies at their play

'Oh bonnie babies, gin ye were mine
I'd cleathe ye in the silks sae fine'

'Oh wild mother, when we were thine
You claethed us not in silks so fine

'But now we're in the heavens high
And you've the pains o hell to try'

She threw hersell oer the castle wall
There I wot she got a fa'