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The actor - who was the wife of the late Good Life star Richard Briers - passed away earlier this week.
The sad news was announced by talent agent Barry Langford, who said in a post on Twitter that she would be "very much missed".
"Sadly my lovely client of 34 years Ann Davies passed away yesterday," he tweeted.
"A superb actress with TV credits including #Doctor Who and #TheSculptress, Ann was devoted to her beloved late husband #RichardBriers and their daughters Lucy and Kate.
"She will be very much missed."
"#RIP Annie," he added.
Sadly my lovely client of 34 years Ann Davies passed away yesterday. A superb actress with TV credits including #DoctorWho and #TheSculptress, Ann was devoted to her beloved late husband #RichardBriers and their daughters Lucy and Kate. She will be very much missed. #RIP Annie pic.twitter.com/9WxgRfsyat
— Barry Langford (@LangfordBarry) April 27, 2022
Davies appeared in Doctor Who in the 60s as a character called Jenny and was in programmes including Z Cars and Family Solicitor.
She also appeared in serials EastEnders, Doctors and Grange Hill. More recent roles include a part in Whitechapel in 2013.
Fans have been paying tribute on social media following news of the star's death.
"Such sad news," one tweeted.
"She was great as Jenny in The Dalek Invasion of Earth."
Another said: "She will be missed. She truly was superb."
"Ah so sad to read this," posted one fan.
"Annie was so very kind and welcoming to me when I was a humble understudy working with Richard."
"Superstar in a legendary Dr Who adventure, and she’ll never be forgotten by the fans!" wrote someone else.
"Those episodes get rewatched a lot in my house."
One tweeted: "Never knew she was married to Richard Briers. Hope you have a loving reunion."
Several posted messages online saying that both Davies and her late husband were "lovely people".
Davies tied the knot with actor Briers in 1956 and they had two daughters together, Kate and Lucy, who is also an actor.
Briers died in 2013.
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