The revival premiered at the Menier Chocolate Factory in fall 2012 and began its West End engagement April 23 at the Harold Pinter Theatre for a limited run through July 27.
The 7 PM screenings will also include backstage interviews with the cast. Tickets for the one-night-only screening are currently on sale at Fathomevents.com.
"This production of Merrily We Roll Along is not only the best I've seen, but one of those rare instances where casting, direction and show come together in perfect combination, resulting in the classic ideal of the sum being greater than the parts," Sondheim said in a statement.
The 1981 musical, which has a book by Furth and a score by Sondheim, is based on Kaufman and Hart's 1934 Broadway play. Merrily travels backwards in time to navigate the bumpy history of three friends who start their careers in show business together.
The West End leading trio of "Old Friends" included Mark Umbers as Franklin Shepard, Damian Humbley as Charley Kringas and Tony nominee Jenna Russell as Mary Flynn.
Also in featured roles are Clare Foster, Josefina Gabrielle, Glyn Kerslake and Zizi Strallen.
The creative team includes designs by Soutra Gilmour, lighting by David Hersey, sound design by Gareth Owen, musical supervision and direction by Catherine Jayes, orchestrations by Jonathan Tunick and choreography by Tim Jackson.
The West End revival was produced by Chocolate Factory Productions, Neal Street Productions, Sonia Friedman Productions, Bob Bartner & Norman Tulchin, Debbie Bisno, Scott M. Delman, Just for Laughs Theatricals and Tanya Link.
Watch the trailer below: