Nearly everybody knows of Stonehenge, the Tower of London and the Natural History Museum. Each year, Visit England’s annual statistics reveal the millions who flock to explore the nation’s best-known attractions. But what of the 20 or so at the other end of the list who see fewer than 300 visitors a year?

From the outside, The Bay Museum on Canvey Island in Essex looks more like a toilet block than a trove of military treasures.

Once a Cold War naval magnetic monitoring station, the diminutive…