Mellor, who wrote hit series including ITV's Girlfriends, Band Of Gold and The Syndicate and was also best known for penning series including Fat Friends which aired from 2000 until 2005 and was turned into a musical, died on Sunday. (May 15).
Jones, who starred as Kelly Chadwick in Fat Friends, said in a statement to the PA News Agency: "I am completely shocked to hear the news of Kay's untimely death. Her contribution to British television was outstanding and I feel privileged to have worked with her.
"Such a down-to-earth, funny, big-hearted person whose brilliance lay in seeing the extraordinary in the day-to-day.
"She was a great mentor to me when I first started writing - and always hugely encouraging of new writers - a real testament to the idea of paying it forward.
"Her series Fat Friends was a massive turning point in my career and I will be eternally grateful to her for what she did for me.
"British television has lost one of its greats. Thank you Kay for all that you gave us. I cannot believe you've gone.
"My thoughts are with Anthony, Yvonne and Gaynor and all the family at this unconscionably sad time."
Councillor James Lewis, leader of Leeds City Council, said: “We are incredibly saddened to hear of the death of Kay Mellor, such a uniquely talented writer who made an immense contribution to the arts both locally and nationally, creating some unforgettable characters and stories which entertained and uplifted millions.
“A Leeds woman through and through, she also broke new ground in bringing imaginative and heart-warming portrayals of life in Yorkshire and the north of England to homes across the country and beyond. She will be very sadly missed and our thoughts and deepest sympathies are with her family and loved ones.”
A statement on the Leeds Grand Theatre facebook page read: "It is with a heavy heart that we have learned of the passing of our good friend Kay Mellor. Leeds born and bred, Kay was a pioneer of northern drama and real-life stories, going where no other female writer, director, and actor had gone before. We’re deeply proud and humbled to have been chosen as the home venue for her two stage premieres Fat Friends The Musical (2017) and Band of Gold (2019) - both of which were huge success stories, as was everything that Kay turned her hand to. The hearts and thoughts of our theatre family are with her family, who we are also blessed to call friends of our theatres."
West Yorkshire mayor Tracy Brabin paid tribute on Twitter.
She said: "Just dreadful news & difficult to take in. Sending all our love from everyone in #westyorkshire to Kay's family, friends & colleagues.
"Our voice of the North, she put working class characters at the centre of her brilliant compassionate, moving & funny stories. Such a loss."
Sir Lenny Henry, who starred in the third series of Mellor's hit TV series The Syndicate, based on a group of lotto winners, tweeted: "I was saddened to hear that Kay Mellor has died.
"I was lucky to work with her on the Syndicate and found her to be incredibly creative, funny and instinctive. She knew what she wanted and knew how to get the best from us as actors. She will be missed. Condolences to her family."
A spokesperson for Mellor's TV production company, Rollem Productions, told the PA news agency: "It is with profound sadness that we announce the untimely and sudden passing of our beloved friend, mentor and colleague Kay Mellor on Sunday May 15 2022.
"We have lost a phenomenal talent and a true luminary. We ask that you please respect the privacy of the family and friends at this time."
Mellor began her career writing plays, worked on Coronation Street and created the award-winning children's drama Children's Ward.
She also wrote BBC One's women's football series Playing The Field and in 2010 received an OBE.
Bafta-nominated series Fat Friends focused on the members of a slimming group in Leeds, and starred James Corden, Ruth Jones, Alison Steadman and Mellor's youngest daughter, Gaynor Faye.
Faye has also starred in Coronation Street, Emmerdale and The Chase on BBC One, a series which she co-wrote with her mother.
Mellor appeared on BBC Radio 4's Desert Island Discs in 2017 and chose The Beautiful South's Perfect 10, the Fat Friends theme tune, as one of her soundtracks, saying: "Every time I heard that I used to get excited and get butterflies."
She explained: "It was such a lovely time of my life, it was a drama that was really important to me because I thought I had something to say about weight and body image."
Band Of Gold, about a group of women from Bradford's red light district, starred Samantha Morton, Geraldine James, Fiona Allen and more.
The BBC's chief content officer, Charlotte Moore, said in a statement: "I'm shocked and deeply saddened to hear that Kay Mellor has suddenly passed away.
"Kay was an outstanding writer and the creative force behind many of the nation's best-loved television dramas.
"She wrote with such heart, humanity, humour and passion with strong female characters often taking centre stage.
"She will be missed and our thoughts are with her friends and family at this difficult time."
Mellor and her husband Anthony were married in 1968 and have two daughters, actress Faye and television producer Yvonne Francas.