Mortuary suppliers have told BBC News they have no stocks of standard body bags left for sale, blaming stockpiling due to the coronavirus pandemic for the shortage.
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 form funeral directors for personal protective equipment (PPE) and the whole industry was worried about how to cope with current death rates.
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 bRead More – Source
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