The West End run of “Million Dollar Quartet” will shutter at the Noel Coward Theater Jan. 14.Following its London engagement of just under a year, the production will go on the road across the U.K. and Ireland. In the U.S. the show is currently playing in Gotham — where it shifted to Off Broadway following a Main Stem stint of 15 months — and in Chicago. A U.S. road production just opened in Cleveland. Comedy hit “Yes, Prime Minister,” the stage incarnation of the TV comedy, is also shuttering, finishing up a limited run at the Gielgud Theater Nov. 19. Stint is the show’s third SRO engagement in London.