The researchers estimated that, if current trends in overweight and obesity rates continue, then by the mid 2020s there could be more than 3,500 additional cases of cancer every year.
"The number of people who are overweight or obese is rapidly increasing both in the UK and worldwide," said study leader Dr Krishnan Bhaskaran, of LSHTM. "It is well recognised that this is likely to cause more diabetes and cardiovascular disease. Our results show that if these trends continue, we can also expect to see substantially more cancers as a result."
Excess weight may account for as many as 41 per cent of uterine cancer cases, and 10 per cent of cancers of the gallbladder, kidney, liver and colon.
The study also found some evidence that, for prostate cancer and for breast cancer in young women, a higher BMI actually reduced the risk.
Precisely how fat could impact upon cancer risk is not fully understood. Dr Bhaskaran said that the variation in its impact across different forms of cancer said it must be affecting risk "through a number of different processes, depending on the cancer type".
Tom Stansfeld, health information officer at Cancer Research UK, said: "This study of over five million people has found new and stronger links between obesity and several different cancer types, highlighting the number of cancers that obesity causes in the UK.
"Although the relationship between cancer and obesity is complex, it's clear that carrying excess weight increases your risk of developing cancer. Keeping a healthy weight reduces cancer risk, and the best way to do this is through eating a healthy, balanced diet and exercising regularly."
- Independent