A blog post by Zoë Harcombe details a long list of problems with the conclusions of this study. She doesn't raise any problems with the methodology of the study, just the conclusions that have been drawn from it.
Specifically to answer your question, no protein does not increase the risk of cancer. The study only claims that it does within a certain age group and within the other age group, it is actually associated with a lower risk of cancer.
Many conclusions can be drawn from the study but only the ones that make animal protein sound bad actually were, which is suspicious:
This is a direct quotation from the article (my emphasis): “Using Cox Proportional Hazard models, we found that high and moderate protein consumption were positively associated with diabetes-related mortality, but not associated with all-cause, CVD [cardiovascular], or cancer mortality when subjects at all the ages above 50 were considered.”
i.e. when we looked at the 6,381 over 50 year olds there was not even an association with protein intake and all-cause mortality, or CVD mortality, or cancer mortality.
There was a relationship with diabetes mortality and protein intake, but the numbers were so tiny (one death from diabetes in one group) that this was not considered important.
And that could have been the headline – “There is no association between protein intake and mortality” – but then there would be no headline.
The results showed that high protein diets are associated with higher life expectancy in over-65s. This means that low protein diets must be associated with lower life expectancy since the average over the entire data set was no association:
Sure enough, the 3,342 people over the age of 65 were far less likely to die from any cause if they were in the moderate or high protein intake group. Cancer mortality for the low protein group was two and a half times the cancer mortality for the high protein group.
The fact that the headlines chose to claim “protein will kill you in middle age” rather than “protein will save you in old age” just highlights the nonsense and bias.
There's also a conflict of interest. The author of the study sells a product that can solve the problems raised by the study:
The study claims to have adjusted for protein in general vs. animal protein to conclude that animal protein is the harmful factor and not protein per se. Call me suspicious, but I always check for conflicts of interest and the lead researcher, Dr Longo, has declared interests in (actually, he’s the founder of) L-Nutra – a company that makes ProLon™ – an entirely plant based meal replacement product.
A comment on the post mentions that three other authors of the study also work for L-Nutra.
The study doesn't have any comparison to smoking but the press release from the lead author of the study does.
That chicken wing you’re eating could be as deadly as a cigarette.
a mortality risk factor comparable to smoking.
It's difficult to determine exactly what this means. It could mean that one chicken wing is the equivalent of one cigarette, meaning that the Daily Telegraph's claim would suggest that a high protein diet means eating 20 chicken wings every day.