I have heard that the Muirhead Tower (at the University of Birmingham) was originally designed for paternoster lifts, but due to legislative changes was built with two regular lift shafts - which were totally inadequate for the volume of students trying to get up and down for every class. They had added a third lift by the time I was there (1997-2002) but it still wasn't enough. I hear it's been thoroughly refurbished since, though.

The Dental Hospital in Birmingham also had paternosters around that time, but only staff were allowed to use them.