Island Location

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http://www.imdb.com/title/tt1531901/locations
http://the-byzantium.wikia.com/wiki/Filming_Locations

It's probably one of the small islands around the filming locations. (UK/Ireland)

http://filmireland.net/2015/11/13/six-horror-films-shot-in-ireland/

The film was shot in various locations including Bray and the Beara peninsula in West Cork as well as the coastal town of Hastings in the UK.

https://en.wikipedia.org/wiki/Hastings_Pier

The pier has featured in many films and TV series, such as the The Dark Man (1951), ITV wartime drama Foyle's War, Kingmaker's "Queen Jane" music video (1993), Ash's "Tracers" music video (2009), and the film Byzantium (2012).