Smoking and obesity are partly to blame for the faster rising rates among women, the charity said.
Its report comes just one day after a leading cancer expert said an effective cure could be just five to 10 years away.
Professor Karol Sikora, former head of the World Health Organisation’s cancer programme, told The Independent that advances in genetics mean doctors should soon be able to prescribe drugs that specifically target an individual’s cancer.
Cancer Research UK’s latest report, which has been released ahead of World Cancer Day on 4 February, revealed that over a period of 20 years, cancer rates will increase by around half a per cent for men and by around three percent for women.
The latest figures show the global burden of cancer has reached an estimated 7.4 million men and an estimated 6.7 million women being diagnosed worldwide each year.
Cancer is the leading cause of death in the world, accounting for an estimated 8.2 million deaths in 2012 and roughly 15% of all deaths.
The four most common cancer types across the world – breast, prostate, lung and bowel – account for more than half (53%) of new cases of cancer each year in the UK.
Among women, rates of ovarian, cervical and oral cancers are predicted to rise the most over the next 20 years.
Sir Harpal Kumar, Cancer Research UK’s chief executive, said: “These new figures reveal the huge challenge we continue to face, both in the UK and worldwide.
“Research is at the heart of finding ways to reduce cancer’s burden and ensure more people survive, particularly for hard-to-treat cancers where the outlook for patients is still bleak.
“We need to keep working hard to reduce the devastating impact cancer can have on so many families.”
Sir Kumar added: “The latest figures show that more than eight million people die from cancer each year across the world. More people die from cancer than AIDS, malaria and tuberculosis put together.
“With more investment into research, we hope to make big improvements over the next 20 years in diagnosing the disease earlier and improving and developing treatments so that by 2034, three in four people will survive their disease.”
The charity is funding research across the country to find better treatments and ways to diagnose the disease early.
In Cambridge, scientists are studying whether DNA from ovarian cancer cells captured in a blood test can indicate how well treatment is working. This research could mean that women are given tailored treatments that are more effective based on the faulty genes driving their disease.
Sarah Toule, head of health information at the World Cancer Research Fund, said of the report: “Cancer is a devastating disease and it is concerning that rates are predicted to rise so sharply in women, especially as so many cancer cases could be prevented.”
She explained that 20,000 breast cancer cases in the UK could be prevented each year if women maintained a healthy weight, were more physically active and didn’t drink alcohol.
“Other cancers that could be reduced by women having a healthier lifestyle include womb and ovary,” she said.
“We hope that people will take the opportunity to make simple lifestyle changes to help reduce their cancer risk - that could be eating more vegetables and fruit, cutting down on the alcohol or doing more exercise.”