Not sure if it's the one you mean, but there was once a Unicorn pub on Wyle Cop, which is now Tanners Wine.
There could of course have been another Unicorn pub in town over the years. I believe the Wyle Cop example I have given closed decades ago. It was also a hotel.
Photos and some local information can be found on one of my Shuts of Shrewsbury threads:
Wine Merchants' PassageI think though member "sgd" will have more info for you and probably the answer.