Brucknell, real name Kimberley Dayle, has performed her tribute act around the world. Bliss appeared on Britain's Got Talent earlier this year and performed during the live semi-finals, despite not securing enough votes from the judging panel.
The Sun claims that the two lookalikes fell out after Brucknell became "great friends" with Bliss's ex-boyfriend Danny Lopez - a professional Johnny Depp impersonator.
However, Brucknell insisted that the pair only got into contact with each other after Bliss, 32, started "bad-mouthing" her.
"Danny looked me up on Facebook to see if I was as bad as she said. He quickly realised I wasn't," she explained. "Anyway, they broke up. She found some emails I'd sent him and went mental. She kicked off with him, it was scary.
"I wanted to remain professional, but I was there for him through their break-up. He's a lovely genuine person."
Bliss and Brucknell's rivalry stems back to their appearance on BBC tribute act competition The One and Only. Bliss said that her rival ruined her chances on the show by slagging her off.
"They are still at loggerheads and refusing to speak," a source said. "Danny really fancied Kitty because he had a thing about Britney Spears. But every time he mentioned her name, Lorna would fly into wild rages."
Bliss declined to comment to the paper.
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Watch Kitty Brucknell's X Factor audition below: