“Hadestown,” Anaïs Mitchell’s musical reimagining of the Orpheus and Eurydice myth, will be staged at the National Theater in London before heading to Broadway next year, the show’s producers said Thursday.The musical has already had two productions, at New York Theater Workshop in 2016, and at the Citadel Theater in Edmonton, Alberta, last year, as it is refined by a creative team led by the director Rachel Chavkin (“Natasha, Pierre & the Great Comet of 1812.”)The show’s developmental journey has been somewhat unorthodox, as the team continues to experiment with the physical production. But, as the competition for space at Broadway theaters intensifies, a number of shows are having multiple productions before landing, including “Come From Away,” which was presented in San Diego, Seattle, Washington and Toronto before New York.Ms. Mitchell, a singer-songwriter, has constructed a folk-and-jazz score that not only retells the ancient myth, but also frames it as a commentary on contemporary economics and politics. The show has not announced a cast for London, but each previous cast was led by Patrick Page as Hades and Amber Gray as Persephone; the cast in Canada featured Reeve Carney as Orpheus and T. V. Carpio as Eurydice.The musical is being produced by Mara Isaacs, Dale Franzen, Hunter Arnold and Tom Kirdahy. The London production is scheduled to run from Nov. 2 to Jan. 26. The producers did not announce specific dates or a theater for the planned Broadway production.