Doctor training is being undermined because of a lack of dead bodies to study, the government says.
Two courses have closed this year because of a lack of bodies
Two courses have already been cancelled this year because of a lack of cadavers and experts said more will be hit if the fall in donations is not reversed.
The government has blamed rising medical student numbers, TV shows and the Alder Hey scandal for the problem.
In the last five years, the number of bodies being donated has fallen from 670 to 600 across England and Wales.
This has been coupled with a rise in medical students - since 2000 eight medical schools and 15 postgraduate anatomy departments for surgeon training have opened.
The Department of Health said people had been put off following the recent Channel 4 TV series Anatomy for Beginners, which showed German doctor Gunther von Hagens dissecting a body.
And potential donors have also said to have cited the scandals over the unconsented retention of body parts at Bristol's Children's Hospital and the Alder Hey Hospital in Liverpool.
A Department of Health spokeswoman said there was a degree of confusion about the issue as the cases were not related to anatomy studies.
She added: "England has an enviable reputation for training some of the best doctors in the world and there is a risk that without these donations students and trainee surgeons will not receive the best training.
"If this downward trend is not reversed medical students will soon not have the opportunity to learn their anatomy from the best "text book" - the real human body."
And Jeremy Metters, Her Majesty's Inspector of Anatomy, added: "We are in difficulties at the moment with a shortage of bodies. If nothing is done we will be in dire difficulties.
"I would like anybody who thinks that they would like to donate their body to medical research to contact their local medical school for information, or they can come to our website."
And the British Medical Association said the declining number of bodies being donated was a problem, but a spokeswoman pointed out medical schools were increasingly able to use technology instead.