Dale Spindel, Kenilworth reference librarian, received this confirmation from Kenilworth, England:
Geoff Symes has passed your query on to me as the Chairman of theKenilworth History and Archaeology Society. ... I came to Kenilworth to teach at the Grammar School, and its Old Boys and Girls were always known as 'Old Kenilworthians'. At one time there was an intermittent Rugby side comprising Old Boys called that. I hope this answers your query. If you get stuck for anything like that again, please don't hesitate to ask. Hopefully, the Society will get into even the 20th century soon & have a website, but not yet!
All good wishes,
So that cinches it. However stuffy and old-fashioned sounding, it's "Kenilworthian" alright.