Ms Davies appeared as Mrs Perks in the Railway Children and as Marj in the valleys-based comedy Stella.
Tony Gardner, who appeared in Stella, wrote on Twitter: "Terribly saddened to hear Deddie Davies has died. She was a truly wonderful person."
Karen Paullada, who also appeared in the Sky 1 series, wrote: "Sad times in this happy Christmas period."
Stella star and co-creator Ruth Jones paid tribute to her "remarkable" co-star.
She said: "Deddie had been ill for a long time and I saw her about a month ago and showed her the Christmas special on my laptop.
"She loved working on Stella. She said it kept her going and she was massively loved by all the cast and crew.
"She was one of those rare people who didn't possess a grain of self pity and whose company always brightened your day.
"A highly intelligent, joyful, talented and spectacularly spirited woman, who was an inspiration to us all."
She added Ms Davies would be "unspeakably missed".
Ms Davies had been a well-known face on TV screens since the 1970s, appearing in shows including The Forsyte Saga, The Bill, Upstairs, Downstairs, Grange Hill and Whitechapel.
Her agents, Brown, Simcocks and Andrews, said the actress also dedicated her time working with charities safeguarding the elderly and also "going undercover" to reveal issues in care homes.
Kelly Andrews, part of the team who represented Ms Davies for about 20 years, said: "She was extremely professional, but she was extraordinary fun and joyous to be around.
"She saw the best in everyone. She wasn't just an actress but an activist - she really cared about it."
Tributes have been paid to Bridgend-born actress Deddie Davies, who has died at the age of 78.