The military has begun helping to deliver fuel to petrol station forecourts to help relieve shortages.
About 200 servicemen and women from the Army and RAF are being drafted in to deliver fuel from depots to forecourts.
They will focus on London and the South East, where the worst shortages remain.
The Petrol Retailers Association (PRA) said on Sunday the crisis was virtually at an end in Scotland, Wales, the North and Midlands, but more than a fifth of forecourts were still dry.
The PRA is scheduled to give a new update on the situation on Monday afternoon.
The government has been criticised for not deploying the military earlier after panic-buying led to chaos and queues on some petrol station forecourts.
More than 65 drivers will start work, with plans to increase this to 200 personnel to be deployed in total, including 100 drivers.
A government spokesperson said there were signs of improvement in average forecourt stocks across the UK, adding that demand was “continuing to stabilise”.
“More than half of those who have completed training to make fuel deliveries are being deployed to terminals serving London and the South-East of England, demonstrating that the sector is allocating drivers to areas most affected in this first phase from Monday,” the spokesperson said.
The crisis began more than 10 days ago when BP said it had run out of petrol in a number of its outlets. That prompted motorists to fill up more than usual, leaving deliveries unable to keep up with demand.
Many sectors of the UK economy, including food firms and petrol retailers, have been affected by a chronic shortage of lorry drivers, which the haulage industry has blamed on factors including Covid, Brexit, an aging workforce, and tax changes.
David Charman, who runs Parkfoot Garage in West Malling in Kent, told the BBC’s Today programme there was a big task ahead to restore supplies.
“This is not panic-buying anymore, this is people that have waited as long as they possibly can and now they have no fuel. We’re having to push cars that are in the queue to get to our site because they’ve run out of fuel,” he said.
“We didn’t have the normal two days of stock underground… because of Covid but we were still managing the situation perfectly well. But now, when we’re all empty, it needs a huge influx of fuel deliveries to everybody, not just to me, to ensure that we can get through this.”