Mortuary vendors told BBC News that they do not have stockpiles of standard body bags for sale, blaming stocks due to the shortage of the coronavirus pandemic.
New stocks from abroad cannot be acquired for many weeks, they say.
The NHS says it currently has adequate stocks, but health professionals report having to wrap the bodies in sheets.
Public Health England said the virus that caused Covid-19 quickly degraded after a patient died.
And there was no specific need to use bags to transport these corpses, although "there may be other practical reasons for using them".
Barber Medical, which has an NHS contract for cadaver supplies, said the availability of zipped corpse bags is a real problem and that they cannot be purchased anywhere.
The company, however, increased the availability of polyethylene bags, known as body bags, and urged any hospital or trust that struggled with supplies to contact it.
A major supplier of funeral directors also told BBC News that he could not get hold of bags because of the stock.
NHS officials and funeral directors were desperate for the bags and "horrified" by official advice that it was safe not to use them, the document said.
Zippered bags are scarce
The bags he sells are made in China, but he said it took six weeks to ship them to the UK and air freight was prohibitively expensive.
The company sought to manufacture its own bags, but failed to obtain the necessary plastic fiber.
The supplier also said it was unable to keep up with the desperate demand from funeral directors for personal protective equipment (PPE) and the entire industry was concerned with how to deal with current death rates.
On Monday, Sally Goodright, a nurse at a hospital in West London, wrote on Facebook, in a post later removed: "We ran out of body bags, but still the dead were coming in from the wards."
The GMB union says some porters have been instructed to transport patients' bodies in sheets.
Helen O & # 39; Connor, regional organizer of Epsom and the St. Helier NHS Trust, said: "We are extremely concerned about the psychological and physical well-being of our traumatized hospital members and struggling to cope with the impact of this pandemic. .
"They are on the front lines, doing the kind of work that would afflict someone and increasingly deal with death."
A trust spokeswoman denied there was a shortage – but there were no dispute sheets being used to wrap bodies, saying there were too many zippered bags to gain hospital trust during the current period, but under the guidance of Public Health England , they were not always necessary.
The guidance says: "Body bags are not considered necessary, but can be used for other practical reasons.
"Putting a cloth or mask over the deceased's mouth when moving it can help prevent the release of aerosols."
BBC News also received a report from a worker at Watford General Hospital, who said sheets were being used to wrap the dead.
When the NHS Trust of West Hertfordshire hospitals was asked whether the use of sheets was appropriate, he replied, "We are involving the organs in accordance with national procedures."
BBC News understands that an emergency stockpile of thousands of body bags held by emergency services will be made available to hospitals and funeral directors.
An NHS supply chain spokeswoman said she had an adequate stock of bags and hopes that more will arrive soon.
An industry body, the British Plastics Federation said UK plastics companies are coming in to help supply equipment in high demand – but have not received any orders for bags.