Some key medicines used in intensive care are "in relatively short supply", the BBC has learned.
Supply of anaesthetic medicines in some areas is "a bit stretched", according to the Royal College of Anaesthetists.
One consultant has told the BBC that supplies are "running low" and alternatives are already being used in intensive care in the Midlands.
The government says it is "aware there is an increase in demand for a number of intensive care drugs".
On 2 April, four leading royal colleges and health organisations asked staff to "act immediately" and use alternatives to some "first line" medications in new guidance on changes to specific anaesthetic drugs facing "pandemic pressures".
Dr Ron Daniels, an intensive care consultant in the West Midlands, says his hospital is "running low" on propofol, a commonly used anaesthetic, and alfentanil, an opioid painkiller which is used in intensive care.
"We are also in short supply of noradrenaline, used to treat life-threateningly low blood pressure, and are now using these drugs only on people who really need them and using older drugs on people who need less intensive support."
Dr Daniels says the quality of care for all intensive care patients, not just coronavirus sufferers, will "likely be lower" as a result as the crisis peaks, and believes there has been too much focus on ventilators.
"With the need of ventilation comes the need for medications to help circulation and blood pressure," he said.
"Without this medication, doctors have no choice but to try to find substitutes," said Dr Chaand Nagpaul, council chair of the British Medical Association.
"This may affect how long patients remain on ventilators, which are in short supply, as well as ultimately impacting their chances of recovery," he added. "This needs to be addressed as a matter of urgency."
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Dr Julia Patterson, founder of medical campaign group EveryDoctor, says she is aware of GPs and palliative care consultants who are also concerned about shortages of diamorphine, in addition to clinicians in ICUs.
She says one ICU consultant in London, who is worried about stocks of muscle relaxants and anaesthetic drugs, has told her that the NHS is working to increase stocks but the situation is "extremely concerning".
The BBC has also been told the chief pharmaceutical officer of NHS England, Keith Ridge, has privately expressed concerns about the availability of some drugs.
"We are seeing some drugs being in relatively short supply", said Prof Mike Grocott, vice-president of the Royal College of Anaesthetists.
He says in centres he has spoken to, "some of the drugs supply is getting a bit stretched, and therefore we may choose to use different types of drugs", but he reassured patients that they would be safe.
"Relative shortages of different drugs - using alternative drugs in their place - is a very normal part of clinical practice," he said.
"We have a variety of different options that we can choose from a menu, if you like, under different circumstances."
'Three years' worth of supplies'
The British Generic Manufacturers Association - which represents UK-based manufacturers and suppliers of generic medicines - says supplies are being moved to areas experiencing shortages.
Its director general, Warwick Smith, said it was seeing four or five times the amount of demand for medicines.
He said one manufacturer recently requested the equivalent of three years' worth of supplies to ramp up production.
In a statement, the Department of Health and Social Care said: "We are aware there is an increase in demand for a number of intensive care drugs and we are working with the pharmaceutical industry to make additional supplies available.
"We are working closely with industry, the NHS and the relevant national expert groups to ensure precautions are in place to reduce the likelihood of shortages."
Last week, Health Secretary Matt Hancock said he was "currently confident" about the supply of drugs.
NHS England has been approached for a response.