Stephen Sondheim’s “Merrily We Roll Along” flopped on Broadway 31 years ago after 16 perfs — and hasn’t been seen on the Great White Way since — but London’s powerhouse Menier Chocolate Factory is staging a revival, and a Main Stem transfer is not inconceivable.

On Nov. 16, 31 years to the day after the original Gotham opening, Menier began previews of its new version of the tuner, which had been regarded as musically satisfying but dramatically flawed; the show has been much-revived in regional theaters, but the new incarnation provides a chance to turn its big-stage reputation — and fortunes — around.

Both Sondheim and Menier a.d. David Babani are playing their cards close to the vest when it comes to the show’s life beyond its limited three-month engagement in London.

Speaking to Variety, Sondheim remains typically judicious regarding future plans. “If the critical reception is enthusiastic enough, I’m sure the cast and the production team would welcome the chance to transfer it.”

While he recognizes that it’s well-nigh impossible for a producing house not to have an eye on possible further life, he asserts it would be foolish to make such plans before a show opens.

That position is shared by Babani. As “Merrily” moves from the rehearsal room into tech rehearsals, he tells Variety, “We have no official plans. At the moment we’re making it as good as possible.”

But the Menier, a 180-seat off-West End house, has serious credibility in ramping up West End and Broadway transfers. This was the venue that produced the revamp of Jerry Herman/Harvey Fierstein’s “La Cage aux Folles,” which went on to a West End run and 2011 triple-Tony-winning success. Its collaborations with Sondheim have been no less successful.

Its scaled-back productions of Sondheim’s “Sunday in the Park With George” and “A Little Night Music” both transferred first to the West End and then to Broadway. “Sunday” picked up nine Tony noms in 2008, while “Night Music” won Catherine Zeta-Jones the 2010 actress Tony, and recouped after a 425-perf run.

The checkered writing and production history of “Merrily We Roll Along,” however, makes the project a slightly different proposition.

Although Sondheim’s score contains some of his most affecting ballads (“Not a Day Goes By,” “Good Thing Going”) and has a uniquely artful construction using reprises and repeated melodies and accompaniments to vivid effect, the dramatic structure has proven a stumbling block.

Based on a 1934 comedy by Kaufman and Hart, it has a plot — about the collapse of idealism among a trio of writers — that famously runs backwards. It opens with composer Frank rich and happy, having, according to old friends and collaborators Charley and Mary, sold out to success. It then runs back to the point at which they all met, shining with hope. Cue heartbreak.

In 1985, four years after Hal Prince’s original production was, as Sondheim remembers “slammed by the critics … there was a vindictiveness in the air,” he and bookwriter George Furth (“Company”) and helmer James Lapine reworked the show for a production at the La Jolla Playhouse in California. They kept the reverse chronology, but ditched the original framing device, tightened events and bolstered the relationships.

“There had always been resistance to the first half-hour of the show, because you’re asked to be interested in a bastard or, rather, a morally corrupt man,” Sondheim says. “Lapine said the sooner that we can show some kind of inner life for the character, the better.”

So Frank’s song “Growing Up” was added, and much of the rest of the book, music and lyrics strengthened.

Seven years later, things were further tightened in a U.K. production at LeicesterHaymarket (the regional house since rebuilt as the Curve, which recently preemed “Finding Neverland”). That’s now the authorized version, and was used for Lapine’s recent Encores staging in Gotham.

It’s also the version being used at the Menier, directed by veteran Sondheim performer Maria Friedman in her helming debut. But Friedman knows the material unusually well: She played Mary in the Leicester production.

Babani argues the production is clarifying the storytelling while heightening the emotions.

“Maria brings real understanding to the central relationships and is bringing that to the forefront in ways I’ve not seen in any other production,” he says.

He also outlines a brand-new opening to the second act with a new dance arrangement turning “Good Thing Going” into a big Broadway-style number. “It gives a real sense of how good these writers are, and why we should care about them,” he adds.

What Babani now cares about is making the run work. The total budget, he says, is between £400,000 and £450,000 ($633,000-$714,000). That covers a cast of 17 and a band of nine, the actors all paid a company wage just above Equity minimum of $520 a week. With only 180 seats and a $55.50 top, it’s very tough nut.

Should the verdict after the Nov. 28 opening be favorable, Babani will look for transfer options. With no first-look deal with the venue, he admits Menier is “looking for the best possible opportunity, whether it be in London or abroad. We are certainly open to offers.”