“A large proportion of sellers continue to express concern that they have no forward visibility of their next deliveries,” he added.
He added: “There are many reports of wet places drying up quickly as the continuation of tankers runs out of kilter with orders.
“The situation in London and the South East remains critical.”
Mr Maderson said over the weekend there had been “a welcome improvement” in the sector, with 10% of non-motorway sites running out of fuel, “not far behind the rest of the country”.
This figure was based on a survey of a quarter of petrol stations.
He cited data from the motoring research charity RAC Foundation which indicated that filling stations were used more intensively in London and the South East than elsewhere.
Mr Maderson said: “Therefore these filling stations need to be refueled more often.
“The need to refill filling stations in London and the South East becomes even more urgent when customers panic, as there are more cars to be filled than the GB average per station.”
The fuel crisis began when demand surged after BP announced on 23 September it would close some of its petrol stations.
The government says it has taken several steps to ease pressure on petrol stations, such as deploying military tanker drivers and exempting the fuel industry from competition laws.
New figures from the Department for Business, Energy and Industrial Strategy show that the average price of petrol in Britain’s court was 137.17p a liter on Monday, up from 2p a liter before the crisis began.
Diesel has increased by 3p per liter to 140.66p per liter in the same period.
These are the costliest average prices of petrol and diesel since September 2013.