Yep. You are spot on. It is the Phoenix Bar & Restaurant. Even now I cant recall it at all...!
One more restaurant is definitely wrong on my list.....
On barker Gate in the Lace market (1990-1996) there was an Italian restaurant where, I think, Anoki restaurant is now.... It may be where Eviva Taverna is, but we think that was a bar not a restaurant... Its not Bistro Live.
Any ideas what this one was called?