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Fuel stocks in London and south-eastern England continued to improve on Wednesday, although drivers remain frustrated by "a crisis" now in its 14th day, a trade body said.
The Petrol Retailers Association said 13% of forecourts in the capital and South East were dry, with 16% having either petrol or diesel and 71% both.
For the rest of the country, 5% are dry, 4% have one grade and 91% both.
Despite military drivers now helping, uncertainty persists, the PRA said.
The PRA represents thousands of independent retailers, many of whom are still in the dark about future deliveries, said the body's executive director, Gordon Balmer.
He said: "Independent forecourts report a complete lack of visibility as to when their next delivery might arrive, and some have been dry for four days and still waiting for a delivery.
"We have yet to see any explanation from the government of the benefits arising from the suspension of competition law between the major oil companies in the delivery of downstream fuel. We need to restore a competitive market with incentives for those who deliver on the job."
On Monday, members of the armed forces arrived at the Buncefield oil depot in Hemel Hempstead to begin work helping to deliver fuel.
Of about 200 military personnel involved, it is reported about 100 are drivers.
The majority of the first tranche of military personnel are being deployed to terminals that service London and the South East, targeting the areas most in need of support.
By the end of this week, it is expected that 150 crews will be delivering fuel across the UK.
Foreign tanker drivers have also applied for temporary visas to fill a shortage of HGV drivers, although it is unclear how many - possibly as low as 27, according to reports.
The government has acknowledged there is a shortage of drivers in the UK, but said the problem is also worldwide and that the long-term solution is for the haulage industry to invest in training rather than rely on workers from overseas.