I remember my parents singing bits of this song, back in the '50s. My recollections are a bit sketchy, but it wasn't the same as the Mike Harding version.
It had refrain lines, thus:
I called on my sweetheart, her name was miss brown
With a heigh, ho, come to the fair.
She was having a bath, and she couldn't come down
With a heigh, ho, come to the fair.
I said "slip on something and come down a tick";
She slipped on the soap and came down pretty quick
With a heigh, ho, (la la la la la la la la la la) in the morning.
Sorry, but that line escapes me; the first four las might have been 'come to the fair' again, but the others are lost in the mists of time J.K.