Bosses took the decision to postpone the upcoming tour dates in Dublin, Belfast and Newcastle to creatively improve the script.
The 56-year-old entertainer, who narrates the play, called on Reckless Entertainment to pay the show's cast and crew.
O'Grady told The Stage: "That is what is killing me. I can afford it, but they [the cast and crew] can't. I feel like screaming out, 'Pay your crew'.
"That is what is sickening me. And there were people on this for whom this was their first job, and I had to tell them it's not like this all the time."
Calling his time working on the musical "bedlam", the chat show host revealed that he contemplated leaving the production during rehearsals, adding: "I also thought, 'If I go, it gives them the perfect excuse to close everything and blame it on me'.
"So I stuck it out, as did the rest of the cast, because we felt a commitment to this thing, which we had been involved in for so long."
O'Grady also revealed that there was no complete script in place when Street of Dreams opened, even suggesting that he had to "cobble stuff together" during the Manchester performances.
On whether he will return to the musical if it returns to the stage, he said: "I don't think I could to tell you the truth, I have been poisoned so much.
"We all feel like we have been thrown down the rabbit hole, gone through some crazy wonderland, and come out the other side saying, 'What was that about?'"
Street of Dreams producers apologised to ticket holders for pushing back the shows, which star the likes of Kym Marsh, Katy Cavanagh and Julie Goodyear.