The Army is ready to help ease fuel supply problems after a fourth day of long queues and pump closures.
Up to 150 military tanker drivers will prepare to deliver to forecourts which have run dry because of panic buying.
The surge in demand came amid fears a driver shortage would hit fuel supply - which is plentiful at refineries.
The transport secretary said there were "tentative signs" of stabilisation in petrol stations and queues would start to reflect this in the coming days.
Grant Shapps said: "Once we all return to our normal buying habits... the quicker we get back to normality."
The Petrol Retailers Association (PRA) said there were "early signs" the pressure on petrol stations was starting to ease,
The organisation, which represents nearly 5,500 of the UK's 8,000 stations, said around 37% of its sites had run out of fuel. That is a big improvement on the situation on Sunday, when two-thirds had run dry.
"With regular restocks taking place, this percentage [of petrol stations with fuel] is likely to improve further over the next 24 hours," it added in a statement.
The UK is estimated to be short of more than 100,000 lorry drivers - causing problems for a range of industries, including food suppliers and supermarkets, in recent months.
The government has said people needlessly buying fuel has led to queues at many forecourts, with fuel running out in some places.
But there are growing calls for key workers, such as health and social care staff, to receive priority access to available fuel after some reported not being able to get to work due to the supply issues.
Daniyal Ahsan, a junior doctor in London, told the BBC he went to 17 petrol stations after work on Monday in search of fuel - but wasn't able to get any, leaving him concerned about how this would affect his patients. He has since been able to fill up his car.
Dr Jane Townson, chief executive of UK Homecare Association, warned that some people who depend on carers for tasks like taking pain medication could die if they are left without help.
Roger Grosvenor, of the East of England Co-op petrol stations, told the BBC the group would create a daily priority hour for emergency workers if fuel supply problems had not eased by Thursday.
Motoring group the RAC said the price of a litre of unleaded petrol had risen by a penny since Friday to an eight-year high - and knew a small number of retailers had been hiking prices amid the soaring demand.
It added it had seen a "sharp increase" in the number of drivers who had broken down after running out of fuel - with engineers attending twice as many breakdowns on Monday than it would normally see over a whole week.
The AA motoring organisation said it had seen a "dramatic rise" in motorists putting the wrong fuel in vehicles compared to last weekend.
Business Secretary Kwasi Kwarteng said the move to place the Army on standby was a "sensible, precautionary step" and if troops had to be deployed, they would temporarily "provide the supply chain with additional capacity" to ease the pressure caused by increased fuel demand.
The BBC has been told that 75 military drivers are on standby initially, and another 75 could be added if needed. They require up to five days of specialised training.
Huw Merriman, a Conservative MP and chairman of the transport select committee, said readying the army was a "good example" of ministers trying to use as many levers at their disposal as possible, and would be used as a "last resort" if the situation did not stabilise in the next couple of days.
But Mr Merriman told BBC Radio 4's Today programme the industry must explain how it planned to fix long-standing driver shortages rather than having the government constantly step in.
"These problems have been there for years because the average age of the driver is 55 years old, they're retiring, and the industry has not made this job attractive. For too long, working conditions have been poor, and those that are willing to tolerate it have been from abroad."
The government has also authorised an extension to special driver licences that allow drivers to transport goods such as fuel.
ADR licences due to expire between 27 September and 31 December will have their validity extended until 31 January 2022, without refresher training or exams.
Labour said the latest response to the fuel crisis was "an admission of failure" and that asking the Army to step up was "a sticking plaster".
Leading fuel companies, including BP and Shell, have sought to reassure the public that supplies remain unaffected at source.
In a joint statement, they said that given "many cars are now holding more fuel than usual" they expected demand would "return to its normal levels in the coming days".
Doctors, nurses, and unions for teachers, prison and care staff have called for essential workers to be given priority for fuel.
Some ambulance trusts have their own fuel pumps in depots and their supplies are expected to be prioritised - but essential workers can still be caught out.
Unison urged ministers to "designate fuel stations for the sole use of key workers" while the NASUWT union called for teachers to be prioritised to safeguard children's education.
But the headteachers' union NAHT said prioritising key workers for fuel was "not a sensible solution as it would be impossible to enforce and could cause more chaos on the forecourts".
And Brian Madderson, chairman of the Petrol Retailers Association, said trying to decide who was and was not an emergency worker and how they would prove this in petrol stations was "very complex" and "hopefully" a last resort.
Asked about the prospect of priority for key workers, Mr Shapps said he would keep a "close eye" on the situation and the government would do "whatever it takes".
Elsewhere, Carol Curry, who needed fuel to drive her husband to a hospital appointment, said she blamed the media for frenzied scenes at the pumps.
"If nobody had said about this, the lorry drivers and everything, then this panic wouldn't have started," she said.
More on the lorry driver shortage
The government has temporarily exempted fuel companies from competition law, allowing them to work together to target supplies at areas most in need.
Temporary visas lasting until Christmas Eve for 5,000 foreign fuel tanker and food lorry drivers, and 5,500 poultry workers, have also been announced.
Nearly one million drivers qualified to drive heavy goods vehicles are being encouraged to rejoin the sector, and some 3,000 new recruits are expected to undertake short, intensive driving courses.
Factors including Brexit, the pandemic, pay levels and an aging workforce have all contributed to a shortage of lorry drivers.
After the UK left the EU, many European drivers returned to their home countries, or decided to work elsewhere because of the additional border bureaucracy and the impact it had on their income.
The pandemic also prompted many foreign drivers to return home and led to a huge backlog in HGV driver exams. Driver shortages have also been seen in EU countries, including Germany and Poland.
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