There are also factors that muddy the waters as people who ate a lot of ultra-processed foods had other behaviours that have been linked to cancer.
They found that if the proportion of ultra-processed foods increased by 10%, the risk of overall cancer increased by 12% - with the risk of breast cancer alone increasing by 11%.
Researchers underlined that sugary drinks and other ultra-processed foods and drinks boost the risk of overall cancer.
In a linked editorial, Martin Lajous and Adriana Monge based at the National Institute of Public Health in Mexico, say this study provides "an initial insight into a possible link between ultra processed foods and cancer" but "we are a long way from understanding the full implications of food processing for health and wellbeing".
Plans are being drawn up to restrict price promotions on foods by the Scottish Government and a new poll by Cancer Research UK has also found 62 per cent of people back the move. (Only 153 people got colorectal cancer, and Touvier says she believes there weren't enough cases to prove an association.) No strong connection was observed between ultra-processed foods and prostate cancer.
If you worry about ever getting cancer, you might want to pass on the processed foods at your supermarket.
Further exploration is needed, but these results suggest that the rapidly increasing consumption of ultra-processed foods "may drive an increasing burden of cancer in the next decades", warn the researchers.
No significant association was found for prostate and colorectal cancers.
Processed foods were found to make up to 50 percent of the average person's diet in several developed countries, the study said, and could be contributing to rising cancer levels.
The researchers of the paper themselves acknowledge that their results "should be confirmed by other large scale, population based observational studies in different populations and settings".
This includes convenience foods, such as mass-produced baked breads and buns, snacks and cookies - plus those staples of modern-day childhood, chicken nuggets and fish sticks, Srour said. "Ultra-processed sugary products were associated with an increased risk of breast cancer".
"Eating a balanced diet, avoiding junk food and maintaining a healthy weight are things we can all do to help stack the odds in our favour", noted Bauld. Nutritionists recommend a diet rich in whole grains, whole fruits and vegetables instead of foods that have little nutritional value.