St. Kilda

... is actually a group of islands, or (as Wikipedia has it) an archipelago. The largest island is called Hirta; other islands include Soay, Boreray and Dun.

St. Kilda was inhabited, possibly for as long as 2,000 years, but this ended in 1930 when the last 36 inhabitants were evacuated. The population had been declining from a peak in the late 17th century, with poor harvests and (particularly latterly) disease related to increased contact with the mainland.

The islands' UNESCO World Heritage Site status, having been initially granted (as the question states) in 1986, was extended in 2005 to include their cultural heritage.