Yes it comes from Bill Caddick. I heard him sing it at the Bacca Pipes FC a year or two ago.
The original text is I guess as noted above (here) where the title is given as 'I Dreamed There Were Unicorns' but I've always known it as plain 'Unicorns'.
I learned it subconsciously from Viv Bjerregaard having heard her sing it many times. Some words may have changed in her singing and again as I sang it from what I remembered. That's the way songs go. I sing 'I dreamed I saw a unicorn' an individual.
It is a magical song I'm very fond of but am afraid I haven't recorded. The change from Am up to A (as I do it) for the chorus is shivery.
I can only record analogue but maybe I could youtube it when I meet up with friends with the right gear.

I have tapestry of a unicorn from Loches, France on my bedside table.

UNICORNS SONG
(Bill Caddick)

We were travelling North to sing and play
And be with friends we'd never met
Been working hard and couldn't sleep
The sky was grey and threatened wet
I dreamed I saw a Unicorn, dreamed I saw him wild and white
His restles beauty filled the world
Like the star that lights the winter's night

He danced and pranced around
Soft as a rainbow round a star
His eyes were soft and sad
And cried

So I wept for the wild and dirty world
To which such beauty now was lost
Cursed the hungry hand of man
That robbed the future at such cost
My head was bowed, my eyes were closed
But in my ears the voices rang
These few words ran deep inside
To my very soul it cried

We never went away
You always knew that we were near,
Remember where to look for us,
You know we were always here

So I raised my eyes to sek them out
But the world was empty all around
Rain cme tumbling from the clouds
To was all dreams into the ground
But when they asked me Why I wept
Like one who for a dead love mourns
The only answer I could give
I dreamed that there were Unicorns

We never went away
You always knew that we were near,
Remember where to look for us,
You know we were always here