The two reviews I found for the show were generally positive, though both thought it was somewhat a work in progress, not surprisingly because...well, it was unfinished and has new material by Chris Bond and Robert Chevara, directed by Mr. Chevara.
Both critics praised the score, by and large, which is nice to see, because several of Bart's later post-Oliver! scores were inconsistent. (I've heard four of the "after" shows, and know of two others, Light in the Piazza, which ran for about a week on Broadway, and the huge flop, Twang!, based on Robin Hood, which ended his career after having invested his own money in it.)
Jane Shilling of The Telegraph wrote about Quasimodo: "Robert Chevara’s production has the air of a work in progress. The musical numbers are tremendous, with the catchy lyrics and haunting melodies of a composer utterly at ease with his ability to write a hit. And there are tantalising hints of the emotional complexity that would flourish if the narrative were given a little more room to breathe.
"At the moment, this feels like an early draft of a much bigger, more ambitious vision. But Lionel Bart would surely have been charmed to know that his musical received its posthumous premiere in the week when the bells of Notre-Dame were restored to the medieval tuning of Quasimodo’s time."
For The Guardian, Michael Billingon said, "Bart's native genius was for jaunty comedy, which is why...the first half of Quasimodo works well." He adds, "But, once we get into the thwarted passion of the eponymous bellringer for Esmeralda, my interest started to wane." But the reviewer brings it around back to what he liked most, "The music, however, acquires a lushness as soon as Bart deals with the romantic yearnings of the doomed outsider. Perhaps he identified too strongly with Quasimodo; more likely his talent was simply not for the tragic."
I tracked down what they call a "trailer" for the show, though it's more a featurette. I wish they focused more on the songs and show, rather than talking heads, but there's enough of the former to get a sense of the production. The sound oddly has a brief issue about halfway through.