I’m pretty sure that the Unicorn bookshop used to be on Duke Street, on the North side just west of where Middle Street joins on the south side of the street.
It was full of tapes of whalesong and books on the paranormal and all that gubbins. A bit like Glastonbury High Street, but in a single shop.
To my naive eyes, it was all stuff and nonsense, but it many ways it was the Yin to the the Hungry Years’ Yang.
I know/knew someone who used to work there, assuming it’s the same place you talk about.
This suggests it isn’t, and my memory is toast: http://www.mybrightonandhove.org.uk/page_id__5395.aspx