"widely held assumption" is a perfectly correct and usable phrase in written English.
You can use it in any context where you want to refer to an idea or viewpoint that is believed by a majority of people. For example, "It was a widely held assumption that the project would succeed, but unfortunately it failed."
The local election results kill off what had been, until recently, a widely held assumption.
She says this very firmly, as if countering a wrong but widely held assumption about 55-year-olds in general.
The widely held assumption that people would volunteer for AIDS-tests in droves once treatment became available was wrong.
There is a widely held assumption that Sec. of State James Baker is working toward a peaceful resolution of the crisis.
The group's forecasts "incorporated the widely held assumption that tax increases and spending cuts reduce economic growth in the short term," Mr. Chote wrote in an open letter.
Only for single people, or married couples without children, does the widely held assumption hold true that you pay a lot less tax in Britain than in France.
As a woman, you grow up with the widely held assumption that it's a sort of inherent done deal that you're going to be a mum.
The researchers, from McGill University in Canada, examined the widely held assumption that social contact – or the lack of it – is linked to mortality.
GÜNTER GRASS wrote a poem restating the widely held assumption that Israel has nuclear weapons and alleging its eagerness to attack Iran is a threat to world peace.
The appeals court also asserted that the requirements for obtaining wiretap authorization under the intelligence law were not that different in a constitutional sense from the requirements for obtaining a warrant in a criminal case, challenging a widely held assumption.
Hapless though the project may have been, it was based on a widely held assumption that financial markets continuously assess the probability of significant economic and political events, including terrorism.
