The monarch made the comments during his first meeting with the prime minster this year.
"I remember thinking that he went to the doctor more than seemed usual, but when I asked if there was a reason why, he quickly changed the subject."
The Duke of Sussex quit royal duties in 2020 and moved to California.
The monarch received his diagnosis after his recent prostate surgery.
"The room blurred, and when I raised my head... gravity took the tears from my eyes and pulled them down my cheeks."
"For more than a year, people had told us that we would know when it 'was time' by the look in our dog’s eyes."
The Charmed star was first diagnosed with breast cancer in 2015. She shared earlier this year that it had spread to her brain.