The report, by the lobby group Science is Vital, is based on a survey of students, postdoctoral researchers and principal investigators.
Of the 750 respondents, 68 per cent named job security as a concern, while 49 per cent cited the impact of short-term contracts - such as unstable personal lives and the loss of expertise from labs - as the biggest problem facing university science.
Science is Vital was set up to campaign for science funding ahead of last year's Comprehensive Spending Review. But its chair, Jennifer Rohn, a postdoctoral researcher at University College London, said funding cuts were not the only threat.
The group invited Mr Willetts, the universities and science minister, to a public meeting about science careers earlier this year. The minister then asked the group to prepare a report summarising its concerns.
Careering Out of Control: A Crisis in the UK Science Profession? describes the responses to the online survey as "a formidable outpouring of frustration, dissatisfaction and genuine regret". It warns that this mood may put PhD students off pursuing an academic career.
"With the current excess of high-quality postdocs, this might seem like a good thing, but it would not take very much for the pendulum to swing too far," it says.
As well as increased funding for science, it calls for a reversal in the current decline in the number of permanent positions below principal investigator level, so that talented senior postdocs, unable or unsuited to becoming PIs, can be retained.
Other recommendations include abolishing restrictive eligibility criteria for postdoctoral fellowships and asking industry to contribute financially to training scientists.
Dr Rohn said the current funding cuts and resulting paucity of permanent positions had thrown chronic problems with the science career structure into sharper relief. She said that it was not for government to impose changes, but she hoped Mr Willetts' interest would raise awareness and provoke discussion.