People could come to harm if the fuel crisis prevents care staff getting to work, Norfolk's adult social care boss has warned.
And James Bullion, director of adult social services at Norfolk County Council, called on the government to oversee national co-ordination so key workers can get petrol and diesel.
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The British Medical Association (BMA) previously said that, as queues build outside stations, "there is a real risk that NHS staff won't be able to do their jobs".
Unison has called on ministers to use emergency powers to "designate fuel stations for the sole use of key workers", while the Royal College of Nursing warned patient care could be compromised.
And Mr Bullion said there are increasing cases of disruption within the care service.
He said: "We need some national co-ordination of 'key worker' fuel pumps, as it will not happen locally and petrol station staff have very few permissions.
"[There are] Increasing reports of care service disruption which could lead not just to inconvenience, but also harm if visits are missed."
Unison's general secretary Christina McAnea said: "Essential staff must be able to get to their jobs so they can continue to provide the services so many rely upon."
But Brian Madderson, chair of the Petrol Retailers Association, said prioritising key workers for fuel was unworkable, describing it as a "very complex situation".
And Paul Whiteman, general secretary of school leaders' union NAHT, said: "Prioritising key workers is not a sensible solution as it would be impossible to enforce and could cause more chaos on the forecourts.
"The only real answer is for the government to do everything in its power to get fuel to pumps and bring this situation to an end."
The government has put army tanker drivers on standby to deliver fuel in order to ease the chaos at petrol stations.
Business secretary Kwasi Kwarteng, said: "While the fuel industry expects demand will return to its normal levels in the coming days, it's right that we take this sensible, precautionary step.
"The UK continues to have strong supplies of fuel, however we are aware of supply chain issues at fuel station forecourts and are taking steps to ease these as a matter of priority."
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