Currently, 12% of cancers in women are linked to smoking, and 7% to being overweight and obese.

But with the number of smokers falling and obesity rates projected to rise, the charity estimates that gap will disappear in 25 years time.

The figures assume that current trends will continue.

Cancer Research UK's projections calculate that by 2035, 10% of cancers in women (around 25,000 cases) could be related to smoking and 9% (around 23,000 cases) to carrying excess weight.

And by 2043, if those trends continued, being overweight and obese could be linked to even more cases of cancer than smoking in women.

Smoking prevention lessons

In UK men, obesity is not predicted to overtake smoking as a preventable cause of cancer until some time later, because more men than women smoke.

Although obesity is more common among men too, obesity in women is thought to be a greater driver of cancers in the female population.

The report says types of cancer linked to smoking include acute myeloid leukaemia, lung, bladder, bowel, cervical, pancreatic and stomach.

Cancers linked to being overweight or obese include bowel, gall bladder, kidney, liver, breast, ovarian and thyroid.

Professor Linda Bauld, Cancer Research UK's prevention expert, said the government must build on the lessons of smoking prevention to reduce the number of weight-related cancers.

She said those who were overweight in childhood were five times more likely to be carrying excess weight as an adult.

Recent figures show that levels of severe obesity during childhood have risen over the last decade in England.

'Act now'

"That's why we are raising awareness of the link between cancer and obesity and calling for measures to protect children, like a ban on junk food adverts before 9pm and for restrictions on price promotions of 'less healthy' products," Prof Bauld said.

She said the decline in smoking was a cause for celebration.

"It shows how decades of effort to raise awareness about the health risks plus strong political action including taxation, removing tobacco marketing and a ban on smoking in indoor public places, have paid off.

"But, just as there is still more to do to support people to quit smoking, we also need to act now to halt the tide of weight-related cancers and ensure this projection never becomes a reality."

More about: Obesity