Nationwide purchases have more than doubled, while in Bristol they are up ten-fold and in London four-fold, according to Superdrug.
Dr Amit Bahl, of the Bristol Haematology and Oncology Centre, said he has also seen a marked increase in patients asking for aspirin.
But he said: “I just hope people follow advice about lifestyle and diet changes too.”
Last week’s research claimed that if everyone aged 50 to 64 in the UK took aspirin for 10 years, 130,357 cancer deaths and 9,473 fatal heart attacks could be avoided over two decades.
Common painkillers could also stop breast cancer recurring in older overweight patients, claims a study from the University of Texas.
But last week’s research led by Prof Jack Cuzick of Queen Mary, University of London, also warned of risks of stroke and internal bleeding.
Dr Chris Paraskeva of Bristol University said: “No one should take aspirin without discussing it with their GP first.”