Daughter of Bond mogul Cubby Broccoli, Barbara, has been involved in the franchise since she was a child.
Speaking on the podcast, she recently recalled: “I do have pretty vivid memories in Japan when they were making You Only Live Twice. [Connery] was always extremely lovely to [me and siblings].
“There is a story about how I got very sick when I was only six years old. They thought I had sleeping sickness.”
Barbara explained how the film was shooting on a remote island in Asia and Connery was the only person on set who had a western bed.
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Barbara said: “So he gave up his bed for me because … I had a high fever and my mother was trying to nurse me.”
She laughed: “So, he was a dad! He wasn’t just a screen icon, he was a dad. He understood what it was to have a child who wasn’t well.”
The Bond boss then took some time to remember the late star, who died almost a year ago in 2020.
She said: “Through the years I would have the occasional conversation with him and he was always just lovely. It’s a huge loss to us and to so many people who were fans of him.”
At the time, the star was in his home in the Bahamas.
His son, Jason Connery, said: “We are all working at understanding this huge event as it only happened so recently, even though my dad has been unwell for some time.
“A sad day for all who knew and loved my dad and a sad loss for all people around the world who enjoyed the wonderful gift he had as an actor.”
Craig said Connery was “one of the true greats of cinema”.
Craig went on: “Sir Sean Connery will be remembered as Bond and so much more. He defined an era and a style.
“The wit and charm he portrayed on screen could be measured in megawatts; he helped create the modern blockbuster.
“He will continue to influence actors and filmmakers alike for years to come. My thoughts are with his family and loved ones.”
James Bond No Time To Die hits cinemas on September 30.
No Time To Die: The Official James Bond Podcast is out now.