Extra administrative and teaching workloads combined with budget cuts are creating a crisis in schools, which are relying on a kind of "Dunkirk spirit" to survive, the report says.
But headteachers at the 18 primary, first and middle schools surveyed kept quiet about internal problems for fear of tarnishing their public image.
"The market economy in which schools now operate makes public admissions of difficulties or low morale potentially damaging to consumer confidence, " the National Primary Centre report, Who Speaks For The Teachers?, concludes. "Any loss of parental or community confidence could result in lost pupil numbers and thus lead to further budget reductions."
The report found that provision in many curriculum areas relied on the goodwill of staff and financial support from parents. Information technology was funded "in large measure" by voucher schemes run by high-street stores and parental contributions, staff were having to fork out for books and basic design and technology components, and school trips were increasingly dependent on special fundraising events.
One school said that a programme to identify special needs had been completely demolished by budget cuts, which last year totalled 2.1 per cent across Oxfordshire.
More and more of the money raised by parents was being used by schools to supplement staffing levels, putting strain on relations between the two. "The parents want to provide the jam, but there isn't any bread," said one headteacher.
Half the schools reported cuts in their maintenance budgets, leaving buildings in one school bearing "all the hallmarks of a service in decline".
Headteachers were working hard to protect their staff by taking on extra duties and providing teaching cover, resulting in illness, stress and disillusionment with the profession.
"It's just an impossible job, I'm afraid." said one headteacher. "A lot of us are feeling it. We're not teaching the children any more, we're just struggling with administration, running the school and managing minuscule budgets. That's the reason I'm getting out of teaching."
The situation, the report concludes, is "an educational version of the Dunkirk spirit which surely cannot be maintained indefinitely".