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Scientists believe that as there is a link across many cancers there "may be a basic common mechanism".
They think, but have not proved, that growth hormones - such as insulin-like growth factors - may be the explanation.
Higher levels of growth factors could do two things. They could result in more cells - taller people are made of more stuff so there are more cells which could mutate and become tumours. Alternatively, they could increase the rate of cell division and turnover, increasing the risk of cancer.
But as Dr Green admitted: "The point is we don't know."
Cancer Research UK's Sara Hiom said: "Tall people need not be alarmed by these results. Most people are not a lot taller, or shorter, than average, and their height will only have a small effect on their individual cancer risk."
Dr Caitlin Palframan, policy manager at Breakthrough Breast Cancer, said: "The big question is why this connection exists. If we can unravel why height affects the risk of cancer it will lead us closer to understanding how some cancers develop."
The researchers suggested that height could also have contributed to increasing cancer incidence. In Europe, average height is thought to have increased by around 1cm every decade during the 20th Century.
They argued that the height increase in that time could have
resulted in a 10-15% more cancers than if heights had remained the same.