The 57-year-old star had part of her tongue removed during the seven hour operation.
Her bandmate Cheryl Baker kept fans updated on her condition on Twitter after hearing from Jay’s husband.
She tweeted: “Jay is stable in ICU Awake and responding well. I will be going back in the morning... she knows you’re all thinking about her and is being very brave.
“She’s in good hands and all the surgery went to plan.”
Cheryl has since revealed that Jay has now been moved from intensive care to a ward in a subsequent tweet to fans.
Skin from Jay’s thigh will be used to reconstruct her tongue, meaning she may never be able to sing again.
Last month Jay revealed how she was diagnosed with mouth cancer just two weeks ago after having a biopsy on her tongue.
She told the Mirror: “I think if they take more of my tongue away the chances of me singing, even talking, will be very slim.”
The Eurovision star said she “got on the train and bawled my eyes out” after being told the diagnosis and added that the “thought of rejoining the band is now keeping me going”.
“Being on stage with them is my happy place,” she said. “Whatever you go through, it doesn’t matter when you are on stage.”
Jay faced a choice between losing her voice or not having treatment, and with a young daughter, she admits it was a no-brainer.
“I have a young daughter, I want to see her grow up, I want to see her get married and see her grandchildren,” she said.
Buck’s Fizz found fame after winning the Eurovision Song Contest in 1981 with ‘Making Your Mind Up’. They and went on to become of the UK’s most-loved pop groups in the 1980s.
Last year the band returned to the charts as The Fizz with a brand new album ‘The F-Z Of Pop’.
Prior to her op, Jay has been touring the UK with original Bucks Fizz members Cheryl Baker, 64, and Mike Nolan, 63.