It's all a bunch of crap... and so very typical of the Daily Mail to report a scaremongering piece of journalism. No-one should ever buy that paper - as they love to sensationalise EVERYTHING! If they don't have you fearing everything (immigration/health/education etc) then they aren't doing their editorial jobs properly.
The simple truth is no-one really knows, apart from the real givens like smoking generally leading to lung and other related cancers, what causes cancer.
I've seen research that says that almost every foodgroup can potentially be a cause. Are you really going to let yourself live in fear of even breathing in case this is a cause too?
Simply put - if you live by these basic rules, you'll probably not go too far wrong:
1 - eat sensibly and in moderation.
2 - have a good balanced diet across the key foodgroups. Check out the NHS/DoH website if you're unsure what this is.
3 - buy the best quality food you can afford. I realise that this varies across many households, but food is not something to scrimp on. Let other luxuries (like drink / cigarettes go, but never scrimp on the food for your family).
4 - ensure you all exercise reguarly and try to ensure that you keep yourself in the best possible state of fitness.
That's about all anyone can reasonably expect you to do and have a decent chance of living a long and healthy (ish) life.
Don't spend anytime worrying about this sensationalist crap. The more we're all talking about it, and the more papers they sell, the more this stuff will happen.
We need to vote with our feet, and IGNORE this topic, and NOT buy their awful paper. Then they might start writing more considered journalism.
Enjoy your week (without guilt or worry!).