The military is helping to deliver fuel to petrol stations as a body representing retailers described a "marked improvement" in the situation across most of the country.
London and south-east England have only had a "marginal" improvement and still face a "challenging" time, the Petrol Retailers Association said.
The organisation said its survey of a quarter of all independent petrol stations in Great Britain on Monday morning showed that about a fifth of them around London and the south-east were without fuel.
For the rest of the country that figure was 8 per cent, said the association, adding that 86 per cent of sites surveyed had petrol and diesel available.
The association represents independent forecourts across the UK and works with about 80 per cent of all motorway services areas.
"Today's figures show the situation is still challenging around London and the south-east, despite a marginal improvement," said Gordon Balmer, executive director of the association.
"Sixty-two per cent of the sites surveyed have both grades of fuel available, 18 per cent have only one grade and 20 per cent are dry.
"Across the rest of the country, however, there has been a marked improvement since yesterday, with 86 per cent of sites having both grades of fuel thanks to steady deliveries and stabilising demand, 6 per cent having only one grade and 8 per cent being dry.
"We are grateful for the support lent by the government through their provision of military drivers, although further action must be taken to address the needs of disproportionately affected areas."
Members of the armed forces arrived at the Buncefield oil depot in Hemel Hempstead on Monday to help deliver fuel.
Soldiers, in uniform and wearing face masks, were at the gates of the Hertfordshire Oil Storage Terminal.
It is understood almost 200 military personnel were due to be posted from Monday, including 100 drivers. By the end of this week it is expected that 150 crews will be delivering fuel across the UK.
Most of the first batch of military personnel are being sent to terminals that service London and the south-east.
Payments for military support are understood to be commercially sensitive.
In a further sign of an improving situation, forecourt operator EG Group announced on Monday that it would remove the £30 cap on fuel sales.
"Following a significant improvement in fuel availability at our sites, with customer purchasing behaviour returning to normal levels in the majority of locations, we are pleased to confirm that we can now remove the £30 cap on buying fuel," the company said.
A representative said there were still "some challenges, primarily in our locations in the south and south-east, but following the actions from the government to secure additional drivers from the military this week, we expect availability issues easing in the coming days".