It began with a brief run in a south London pie and mash shop, with the production coming to an end because the 109-year-old Harrington’s in Tooting had to close for refurbishment.

But from those first Selkirk Road performances in front of a few dozen people squeezed together while the actors clambered on tables between them, Tooting Arts Club’s (TAC) production of Sweeney Todd transferred this week to a theatre off Broadway, opening with a performance that captivated the city’s hard-bitten critics.

“Miniature but powerful,” said the Stage in a five-star review; Time Out judged the cut-throat musical “bloody brilliant”. Most impressively of all, among those taking in the opening night was the show’s legendary 86-year-old composer and lyricist, Stephen Sondheim. Not bad for a production which had to crowdfund a third of the budget for its original south London run through Kickstarter.

The journey from Tooting to Manhattan has, admitted producer Rachel Edwards on the morning after Wednesday’s opening night, been “an absolute rollercoaster”.

Edwards – born and raised in Tooting – formed TAC five years ago because she wanted to bring quality productions to the somewhat unglamorous south London suburb. The company has never had a permanent home – previous event venues included Tooting Bec lido – but is now based at Barrow Street Theatre in West Village, New York, which she described as “the perfect fit”.

The set is a faithful recreation of Harrington’s and the action is still performed around and between those sitting at trestle tables, though the audience – 130 rather than the original 32 – is a little larger.

It is not the first time the production has had an unexpected glamorous transfer, after Sondheim, having caught wind of the tiny show’s critical acclaim, turned up at Harrington’s in 2014 on the closing night of its original Tooting run. He raved to his friend, theatre producer Sir Cameron Mackintosh, who offered Edwards a disused space he owned on Shaftesbury Avenue, a move described by the Guardian at the time as “one of the most remarkable West End transfers in living memory”.

The legendary composer and Edwards stayed in touch, and his visit on opening night was the third time he had seen the New York production, in various stages of readiness. Her cast must be rather blase about having Sondheim in the audience? “I don’t think you ever get over singing the lyrics written by the man himself three inches from his face, but I think they are a little more relaxed than when he first turned up in Tooting,” said Edwards.

“It’s thrilling and humbling and absolutely extraordinary to bring it to New York and have him in the audience, I’m not going to lie.”

The New York audience can tuck into pie and mash before the performance starts. Photograph: Joan Marcus/AP

The production may no longer be in a pie shop, but New York audiences at Sweeney Todd – which centres on a throat-slashing barber whose victims find themselves served up encased in pastry – can still enjoy the traditional London pie and mash. Theatregoers can order the meal with their tickets and tuck in, on tables shortly to be used in the performance, before the production starts. New Yorkers, says Edwards, “are loving the pie and mash”, no doubt because rather than the (not universally beloved) London version, these are created by Obama’s former White House pastry chef Bill Yosses.

For the Broadway critic Alexis Soloski, the production’s popularity may be partly explained by an increasing trend towards more “immersive” theatre, “though this is unusual because it’s taking a traditional play, one that’s traditionally performed in a proscenium space, and making it immersive.

“To retrofit a traditional proscenium show, borrowing the immersive element by kitting it out as a pie and mash shop, and serving food before the show, I think that’s such an interesting choice. When you see the show and you figure out what’s in those pies, it’s got to give you a very queasy feeling, realising what you’ve just [supposedly] eaten.”

The veteran London critic Michael Coveney, who reviewed the Shaftesbury Avenue production (“the pies were disgusting, but perhaps deliberately so, because Mrs Lovett does sing that she has the worst pies in London”) agrees about the refreshing potential of staging a well-known musical in a format that audiences consider “immersive and wraparound”. “People increasingly think of theatre as an event. We are so inured now, with social media, to consuming our information and culture on our own, theatre remains a communal experience, so that unique thing about it is even more important today.”

Edwards may be the toast of New York’s critics, but she can’t wait to take her small company back to Tooting. At the champagne opening party on Wednesday night, she said, she found herself thinking about Harrington’s and its owner, Beverley Mason, “because the only reason we are here is because they said yes. When I walked in and asked her, she had no idea who I was, but she said a straightforward yes. I’m very grateful to her, and I’m very proud that I can fly the Tooting flag. So we’re very keen to get back and crack on with whatever may be next.”