Mortuary suppliers have told BBC News they have no stocks of standard body bags left for sale, blaming the shortage on stockpiling due to the coronavirus pandemic.
New stocks from overseas cannot be sourced for many weeks, they say.
The NHS says it currently has adequate stocks but health workers report having to wrap bodies in sheets.
Public Health England said the virus that caused Covid-19 degraded quickly after a patient had died.
And there was no specific need for body bags to be used to transport these corpses, although "there may be other practical reasons for their use".
Barber Medical, which has the NHS contract for mortuary supplies, said availability of zipped mortuary bags was a real problem and they could not be sourced anywhere.
The company has, however, increased the availability of polythene bags, known as body pouch bags, and urged any hospital or trust struggling with supplies to contact it.
A major supplier to undertakers also told BBC News it could not get hold of body bags, because of stockpiling.
NHS trusts and funeral directors were desperate for the bags and "horrified" by the official advice it was safe not to use them, it said.
The bags it sells are made in China but it said it took six weeks to ship them to the UK and air freighting them was prohibitively expensive.
The company has looked into making its own bags but cannot source the required plastic fibre.
The supplier also said it was unable to keep up with the desperate demand from funeral directors for personal protective equipment (PPE) and the whole industry was worried about how to cope with current death rates.
William Quail, managing director of mortuary supplies firm Mortuary Equipment Direct, has hired a team of people to sew between 150 and 200 body bags a day, but he said he was struggling to get the products to hospitals due to bureaucracy.
He said at £57.50 the bags were more expensive than those made in China, which he said cost £9.
"Dignity is the word," Mr Quail said. "I don't think £57 would seem very much if it was your mother or father. I understand they are more expensive but what is a body worth to treat it with respect."
On Monday, Sally Goodright, a nurse in a west London hospital, wrote on Facebook, in a post later removed: "We ran out of body bags but still the dead were arriving from the wards."
The GMB union says some porters have been told to transport the bodies of patients in sheets.
Helen O'Connor, a regional organiser at Epsom and St Helier NHS Trust, said: "We are extremely concerned about the psychological and physical wellbeing of our hospital members who are traumatised and struggling to cope with the impact of this pandemic.
"They are on the front line, doing the type of work that would distress anyone and increasingly dealing with death."
A spokeswoman for the trust denied there was a shortage - but did not dispute sheets were being used to wrap bodies, saying there were plenty of zippered body bags to get the hospital trust through the current period but under Public Health England guidance they were not always necessary.
The guidance says: "Body bags are not deemed necessary but may be used for other practical reasons.
"Placing a cloth or mask over the mouth of the deceased when moving them can help to prevent the release of aerosols."
BBC News also received a report from a worker at Watford General Hospital who said bedsheets were being used to wrap the dead.
When the West Hertfordshire Hospitals NHS Trust was asked if using bedsheets was appropriate, it responded: "We're wrapping bodies in line with national procedures."
BBC News understands an emergency stock of thousands of body bags held by emergency services will be made available to hospitals and funeral directors.
An NHS Supply Chain spokeswoman said it had an adequate stock of body bags and was expecting more to arrive soon.
Industry body the British Plastics Federation said UK plastics companies were stepping in to help provide equipment in high demand - but it had not received any requests for body bags.