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The star was due to perform at the event this weekend but said she is “not emotionally, mentally or physically able to” as she mourns Harding, who died this month at the age of 39 after battling breast cancer.
She posted a moving message on Instagram telling fans she was sorry but that her heart was “heavy” and that she needed “some time to sit with my feelings”.
"Saying goodbye to somebody you spent such a massive piece of your life with is like nothing else," wrote Cheryl, 38.
“My heart is heavy.
"Grief is such a harsh experience and an absolute rollercoaster of emotions.
“Questions without answers and pain without resolve.
“So tumultuous and constant.”
“With that said I am so sorry but I really am not emotionally, mentally or physically able to perform for you at this Birmingham Pride,” she went on.
“I apologise wholeheartedly and I can only hope for your understanding (I promise I will make it up to you somehow).
"I feel now I just need some time to sit with my feelings and process the grief."
"Nothing prepares you for this bit," she added.
Read more: Sarah Harding's 12 greatest moments
Harding revealed last August that she had been diagnosed with breast cancer and that it had spread.
Her mother Marie announced on 5 September that she had passed away, saying her “beautiful” daughter was “a bright shining star”.
Countless stars paid tribute to the singer, with Cheryl describing her as “stunning, unique, crazy, quirky, kind and soft-hearted”.
Bandmate Nicola Roberts described Harding as “Electric girl” in a moving Instagram post, adding: “You made us. You gave it everything and still with a smile.”
Watch: Nadine Coyle wants a visit from Sarah Harding's spirit