A survey of 2,000 for Cancer Research UK suggests 40% might delay getting symptoms checked out because they are worried what the doctor might find.
Yet early diagnosis is key to treating cancer successfully.
Data suggest that if Great Britain matched Europe's best cancer survival rate 11,500 deaths could be avoided.
Prof Peter Johnson of Cancer Research UK said: "Our report highlights just how much more we have to do to raise awareness about the early signs of cancer.
"If patients are diagnosed when the cancer is still in its early stages before it has had a chance to spread to other parts of the body it is more likely that treatment will be successful. That is why it is so important for people to be aware of things that might be early signs of cancer."
The poll findings suggest a quarter of patients might delay seeing their GP with symptoms because they fear they could be wasting their doctor's time.
And many do not recognise which symptoms may suggest cancer.
More than three-quarters of people asked to list possible warning signs and symptoms of cancer failed to mention pain, coughing or problems with bowels or bladder.
And more than two-thirds also failed to list bleeding.
Prof Johnson said: "Of course we are all frightened of hearing that we may have cancer. But people need to know that catching the disease early gives them much better odds of surviving it.
"The best precaution anyone can take is to be on the lookout for any changes in their bodies that seem unusual for them and to get them checked by a doctor.
"We know that in many cases these things won't turn out to be cancer. But don't take the gamble of missing out on early diagnosis."
Cancer Research UK has teamed up with Tesco to raise £10m to fund 32 early diagnosis research projects across the UK. Cancer Research UK leaflets on early signs of cancer will be on display at the store's checkouts.