"Tragically she is stuck in quarantine in Australia, having just flown in from New Zealand last week.
"She was unable to see or talk to him at the end of his life and there is a chance a funeral may not be held."
Jack was "full of life", "funny, charming and a joy to be around", she added.
"He was still working full-pelt, currently coaching on the new Batman."
McCullough added that Jack passed away in hospital in Surrey on Tuesday "of COVID-19".
The veteran actor’s film credits included Star Wars: Episode VIII — The Last Jedi in which he appeared as General Ematt, as well as Solo: A Star Wars Story and Star Wars: Episode VII — The Force Awakens.
Jack's clients for his dialect coaching included the actors Robert Downey Junior and Chris Hemsworth.