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The Liberty X star, 42, battled substance abuse problems for years, and previously revealed she used to buy vodka instead of doing the school run.
At one point she was told she would die if she didn’t do something about it.
Price and other friends stepped in and helped to organise a stint in rehab at The Priory last year, and Heaton is now sober.
Speaking on the One For The Road podcast, Heaton said things changed for her after Price came to see her following a heavy night.
"I was really hungover that morning and I remember just needing more,” she said.
“My husband was done done, I think he was close to walking out. He was done. I came in at 6am, I couldn't find my key… I went to my friend's house and Kate came to see me, and she was like a different Katie."
Price, who had completed her own stay at The Priory, asked Heaton: “Do you want what I’ve got?”
The singer said “yes” and was at the rehab centre 48 hours later.
“The best thing that I could have done was say yes,” she said.
“I didn’t actually think it was going to happen."
“I was just gonna die… I didn't know there was a solution," Heaton went on.
"But Kate, Hugh - my manager - and a couple of friends made it happen. They got the funds together and they got me the consultation."
The star said the rehab stay was a turning point.
"I remember being absolutely done for maybe a couple of months, but the absolute 'done, done' was probably a week in The Priory," she said.
Watch: Michelle Heaton talks about her first sober Christmas