"serious proportion" is correct and usable in written English.
You can use it to describe the degree to which something is serious or significant. For example, "The fire caused a serious proportion of damage to the building."
"The wrecking of phone boxes," Mr. Thomas writes at one point, "assumed serious proportions by 1962".
After the war the nation found itself confronted with a crime wave of serious proportions.
David McDonald, co-director of the Municipal Services Project, said the government's own reports have portrayed a "crisis of serious proportions".
Unfortunately, by 1801 merchants were doubting the value of the currency they received, and inflation assumed serious proportions.
In the early 1980's it was recognized that asbestos litigation was going to cause a hemorrhage of serious proportions in the assets of asbestos-insulation manufacturers & their insurers.
When Hadrian left Rome in 134 for his final journey abroad, it was to resolve a problem of serious proportions in Judaea.
At the same time, millions of refugees from the eastern portion of Bengal which had become East Pakistan (now Bangladesh)—flocked to Calcutta, aggravating social problems and increasing overcrowding, which had already assumed serious proportions.
That's big news, as it's tangible evidence that youth oriented online social networking is a market driver of serious proportions.
I'm an alcoholic in serious proportions and I need help physically and mentally.
But meanwhile, CNBC has been also touting the views of another Trump supporter and confidant, the activist investor Carl Icahn, who has been critical of the Fed no matter what it has done on rates and who has been confidently predicting--every quarter for the past year--an economic and market breakdown of serious proportions.
