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Porridge and Rising Damp actor Richard Beckinsale died of a heart attack in 1979 at the age of 31, when Kate was just five.
The star often remembers her dad on social media and has now paid tribute to him with the poignant side by side pictures.
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The first snap shows Kate beaming at the camera, and is followed by an image of Richard smiling in her direction.
“Just wanted to post this so we are smiling side by side in my feed. The best part is he’s looking at me, actually, in his photo,” she said.
“So happy to carry on the family smile.”
Kate’s fans and friends were utterly charmed by the gesture.
“Awwww he was so handsome and he was look (sic) at you! That’s so lovely,” said TV star Davina McCall, while This Morning’s Eamonn Holmes posted a string of prayer emojis.
Actor and comedian Sanjeev Bhaskar posted a heart emoji and said: “When I was a kid, I thought he was by far the best looking comedy actor on the box.”
Kate often marks milestones such as anniversaries and Father’s Day with touching posts on social media, and has previously told how her dad's death was a “terrible loss”.
Speaking in 2013, she recalled: “It’s so weird as a five-year-old to look out in the street and see people reading the paper and crying while you’re crying and your mum is crying and your granny’s crying.”
Richard starred as prison inmate Lennie Godber in Porridge, which aired from 1974 to 1977. At the same time he played medical student Alan Moore in the hit sitcom Rising Damp.
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