The 22-year-old country singer is believed to have embarked on a relationship with the `My Week With Marilyn` star after meeting at the auditions for a film adaptation of `Les Miserables` last October.
A source said: "They hung out in New York city with the movie`s execs."
British-born Eddie, 30 - who attended Eton College with Prince William - kept in touch with Taylor when he returned to the UK, where they met for drinks in January before reportedly spending the night together at her hotel suite.
But with Taylor based in Nashville, Eddie is said to have pulled the plug on their fledgling relationship because of the distance.
The source told US Weekly: "Taylor loved this image of a British boyfriend. Eddie`s not interested in a long-distance relationship.
"The elements were against them. It`s a shame."
The bad news has not stopped their for Taylor - who has also been linked to actors Taylor Lautner and Jake Gyllenhaal, and musician John Mayer. She lost out on the role of Eponine to actress Samantha Barks, who played the character in the stage version of `Les Miserables`. Samantha will now star opposite Eddie, who is set to portray Marius.
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