The company, founded by director/playwright Richard Maxwell, has previously been presented as part of BITE in 2001 with two productions, House and Boxing 2000, and again earlier this year with Drummer Wanted.
Commenting on the cancellation, Barbican artistic director Graham Sheffield and Head of Theatre Louise Jeffreys said: "The Barbican has been a committed supporter of Richard Maxwell and his work with New York City Players since we first encountered it in 2000. His previous seasons here have started to build a substantial reputation for him in this country and we are sure that his work will continue to gain in popularity over here."
And yet, they went on, "Having now had the opportunity to attend early performances of Henry IV Part One in New York, we do not feel that it is appropriate for inclusion in the Barbican's programme. We have taken this decision very reluctantly, however, we are confident that it is right in this particular instance. This does not affect our admiration for the work that Richard has done in the past or our faith in the work that he will create in the future, and we are discussing future Barbican appearances with him."
According to a report in the New York Times, the recent one-week run of this production at New York's Brooklyn Academy of Music (BAM) was greeted with "an avalanche of scorn", with a representative of the academy estimating that a fifth of the audience walked out. One attendee was said to be threatening legal action if his ticket price was not refunded: "It would be some small comfort to be the first person in New York theatre history to file suit for abuse of Shakespeare."
New York reviews have also been poor. Variety's Christopher Isherwood wrote: "This was simply bad Shakespeare. Very bad Shakespeare. Indeed, risibly bad Shakespeare". Maxwell, for his part, responded by telling the New York Times: "It is not my intention to be 'bad' or 'radical'."
At the Barbican, tickets have been taken off-sale and full refunds are being offered. For further information, contact the Barbican box office on 0845 120 7500.
- by Mark Shenton