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."

Four mountain rescue teams were called to separate incidents at the summits of Corn Du and Cribyn.
One person is being treated at Swansea's Morriston Hospital for burns. The other is at Prince Charles Hospital in Merthyr Tydfil.
Some rescuers were training in the area when the incidents happened.
An RAF Sea King from Chivenor was sent to aid two casualties on Cribyn and road ambulances and police were also sent to the scene.
Brecon Mountain Rescue Team were ending their exercise due to the electric storm when they received a call-out.
Its team doctor reached the first male casualty on Corn Ddu within 35 minutes.
Spokesman Mark Jones said passing cadets who had been on the summit at the time of the strike had already started resuscitation when the rescue doctor took over.
"I've been in Brecon Mountain Rescue for 30 years and I've never known anything like this," he said.
"It is exceptionally unusual, and for multiple people to be hit in multiple strikes on different peaks - it is very, very rare."
Three other mountain rescue teams - Central Beacons, Longtown and Western Beacons - were also called out.
A Dyfed-Powys Police spokesperson said: "As a result of these incidents, two men have sadly died, one man is in a serious condition in hospital and another man is in hospital but did not sustain serious injuries.
"Officers have informed the next of kin of the deceased men."

The 55-year-old tweeted from the hospital in Tooting to thank the professionals who "saved his life".
Moore won 64 England caps between 1987 and 1995, played for the British and Irish Lions, and trained as a solicitor while pursuing his rugby career.
The former England hooker now works in the media.
Tributes have been paid to Bridgend-born actress Deddie Davies, who has died at the age of 78.
[NEXT_CONCEPT]
Two men are being treated in hospital after lightning strikes in the Brecon Beacons which killed two other men on Sunday.
[NEXT_CONCEPT]
Former England rugby international Brian Moore is recovering in intensive care at St George's hospital in London after suffering a heart attack.