The same study found that more than half of men in the general population are blind to the serious risk posed by having close relatives with the disease.
Men are 2.5 times more likely to develop prostate cancer if the disease has affected their father or brother.
Prostate Cancer UK, which carried out the research, also found that only one in 10 GPs are likely to ask their male patients if any of their relatives have had prostate cancer.
The charity's chief executive Angela Culhane said: "There's no denying that GPs in the UK today face tremendous pressure to start conversations with patients regarding an ever-growing list of medical conditions.
"We need men to feel empowered to take control of their own health, find out their family history and pro-actively ask their GP whether they need tests for the disease due to their risk of developing it. Currently this isn't happening nearly enough and the increased risk due to family history of prostate cancer is being dangerously overlooked by both men and their GPs.
"Too many men are walking around completely blind to the serious danger they could face. This must change."
Each year more than 40,000 men in the UK are diagnosed with prostate cancer and around 11,000 die from the disease.
The new study was based on an analysis of Public Health England cancer data and an online survey of 1,901 adult British men.
The findings were released in the run-up to Father's Day, next Sunday.
Ms Culhane added: "Every single one of us can do our bit to reduce the number of men who lose their lives to prostate cancer every year in the UK.
"This Sunday, Father's Day, ask your dads, brothers, grand-dads, husbands, partners and friends about prostate cancer and urge them to book an appointment with their doctor if they have a family history of the disease."
Prostate cancer can be successfully treated if caught in time, but the disease often displays no symptoms in the early stages.
As well as a family history of the disease, two other important risk factors are being aged over 50 and black ethnicity.
