Golden Globe winning actor Hamm, who played Don Draper in 1960's drama Mad Men, stars alongside Jessica Brown, Hayley Atwell, Oona Chaplin and Daniel Kaluuya.
Filming of scenes set in a traditional country market take place on Sunday 22 and Monday 23 in Tejeda village. Up to 60 locals will also appear as actors and extras.
Black Mirror is a UK drama series that often explores the dark side of technology and the media. It has been compared to "The Twilight Zone" for the Millennial generation and is written by the rather splendid British satirist and broadcaster Charlie Brooker.