The show, called I Can't Sing, has already been delayed by several days as a result of technical difficulties in staging the production at the London Palladium.
But when preview performances finally began on Wednesday, theatregoers found themselves waiting 47 minutes at the interval with staff handing out free drinks to lessen the blow.
The team behind the musical, which has the financial backing of Simon Cowell, said they were "ironing out" the problems, but conceded there was "still work to do".
Hill's show features Nigel Harman as a Cowell-like figure and there are cartoon-ish characters which take in elements of many of the people associated with the show over the years such as Cheryl Cole and Louis Walsh. There is also a dog called Barlow - a reference to panellist Gary Barlow.
Producers of the show acknowledged there was still work to be done but pointed out that the preview period before an official opening is traditionally a time when performances are refined.
In a statement, they said: "We've had an absolutely terrific response from our preview audiences, with standing ovations each night so far.
"We have a huge and ambitious set, which is thrilling our audiences when they see it, but we're aware that the turnaround between acts needs to be quicker and our technical teams continue to work extremely hard on shortening it.
"The preview period for any new West End show is, by its nature, a time for ironing out any issues and we fully recognise that there's still work to do on the interval length, which is getting shorter all the time, and we thank everyone for their patience."