Researchers said patients of this age who have already suffered heart attacks or stroke should still take the daily tablet, but should also take an extra drug to reduce the risk of bleeding.
And they said millions more pensioners who take aspirin daily “as a health choice” to cut their risks of heart disease should consider weaning themselves off the drugs.
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.
Around 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.
Prof Peter Rothwell, lead author from the University of Oxford said aspirin was causing around 20,000 bleeds annually – and causing at least 3,000 deaths.
Prof Rothwell said: “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.