Star's life-saving offer to mother
But Melissa Bell said she refused the offer because she did not want her daughter to sacrifice her chances of having a family - a possible side-effect of the operation.
She said: "I need a new kidney. Alex offered me hers and was very serious about it, but if you take a kidney from a woman who hasn't had babies, you take away her chance of having a family.
"That's more than robbery, it's downright wicked."
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Hide AdMrs Bell, who is on a waiting list for a kidney transplant, said another of her four children, David, 23, had offered his kidney and doctors were carrying out tests to see if it was suitable.
Burke won the TV reality show in 2008 and her debut single, Hallelujah, set a record as the fastest-selling download single in Europe.