Doctors stressed that no one should come off the pills quickly, or without consulting their doctor, as doing so would create an immediate risk of heart attacks.
About 40 per cent of pensioners in the UK take aspirin daily, researchers said, with numbers evenly split between those who have already suffered a heart attack or stroke, and those taking it as a precaution.
Many doctors extol the benefits of the drug, which can protect against both heart disease and cancer.
It has long been known that the pills carry a risk of gastro-intestinal bleeding. But the new study, published in the Lancet, suggests the danger increases far more sharply with age than was thought.
Professor Peter Rothwell, lead author from the University of Oxford said aspirin was causing about 20,000 bleeds annually and at least 3000 deaths.
"We know clearly from trials and other research that aspirin is effective at preventing recurrent heart attacks and strokes. Twenty per cent of potential recurrent heart attacks and strokes are prevented by aspirin," Rothwell said.
"Nevertheless, there are also about 3000 excess bleeding deaths attributable to blood-thinners like aspirin across all age-groups," he said, warning that the risk of serious bleeding is much higher among the over-75s.
All patients who have had a heart attack or stroke should still take aspirin, he stressed.
But those above the age of 75 should also be prescribed a proton pump inhibitor, which would reduce bleeding risks by up to 90 per cent.
And those without such medical histories should consider coming off aspirin altogether, he suggested - but not without taking medical advice.
This story was originally publish by The Daily Telegraph.
