Scopus Affiliation Identifier
Basically each institution is given a unique number. I am not sure you can search for this, but there is an "affiliation" search available. I tried this, putting in Leicester. This found eleven institutions:
University of Leicester
Leicester Royal Infirmary
De Montfort University
Leicester General Hospital
University Hospitals of Leicester NHS Trust
MRC Toxicology Unit
National Space Centre
Leicester Medical School
University College of Leicester
Under each, the variant names are listed.
You can choose to see the references associated with any of these names, the idea being that every reference from that institution will be found, regardless of the form of name used in the reference.
This seems to work well, although you can't go that extra stage and search for departments using standardised names. This is always a tricky sort of search, but I guess standardising it would be too tricky?
Scopus is at www.scopus.com (logging in will be necessary off campus), and the Affiliation search is under the Search button. You can also do Affiliation searches from the Basic and Advanced Search screens, using the drop down box.