I only know the version by Archie Fisher - he sings it under the name Mally Lee. Apparently its an old Edinburgh song about Mrs Mally Sleigh who married Lord Lyon Brodie of Brodie in 1725 or theierabouts. These words are more or less Archies with a few alterations Ive picked up on the way.

When Mally Lee cam doon the street,her Capuchin did flee
She coost a look behind her, to see her negligee

And were all going east and west, were a going aye agee
Were all going east and west, a-coorting Mally Lee

All along the Canongate were beaux of ilk degree
And mony an ane turned roond tae look at boony Mally Lee

From Seatons Land a countess fair looked ower a window hie
And pined to see the gently shape of bonny Mally Lee

The dance gaed through the palace hall, a comely sight to see
But nane was there sae bricht and braw as bonny Mally Lee

The prince cam oot frae mang them all, wi garter at his knee
And danced a stately minuet wi bonny Mally Lee

Hope this helps,
cheers
John