The charity Prostate Cancer UK backs the call, saying doing more checks could potentially save thousands of lives each year.
Spokeswoman Chiara De Biase said: "One in eight men will get prostate cancer, but there's currently no screening programme for the disease.
"If your dad or brother has had prostate cancer, or you're black, you have the highest risk of getting the disease, and we strongly recommend you talk to your GP about testing from 45.
"Right now, you need to be aware of this and bring it up with a GP yourself. As prostate cancer often has no symptoms in its earlier stages this is leading to too many men getting a late, incurable diagnosis - like Sir Chris."