What Golden Globe-nominated British series was remade as Viva Laughlin? The answer is Blackpool. The BBC musical drama serial Blackpool was created by Peter Bowker and later served as the source for the American adaptation Viva Laughlin.
Blackpool follows the owner of a seaside amusement arcade whose life is disrupted by a murder investigation. The series combines crime drama, family conflict, and musical performances, with David Morrissey and David Tennant among its principal stars.
The program was broadcast in the United States under the title Viva Blackpool. A feature-length follow-up also used that title, which likely caused confusion with the name of the original series. Viva Laughlin retained the same basic premise but relocated the story to a Nevada casino setting.
Blackpool was nominated for a Golden Globe in the miniseries or television-film category under the title Viva Blackpool; it did not win that Golden Globe. Thus, the question's award wording is inaccurate, but the intended series answer is Blackpool.