Ministers have said they expect the fuel crisis to improve across the country, with the first troops driving tankers expected to appear on the roads "in the next couple of days".
Business Secretary Kwasi Kwarteng said the situation appeared to be "stabilising" with most people "behaving quite responsibly".
He said: "It takes, sometimes, a few days to get troops on the ground. I think in the next couple of days you will see some soldiers driving tankers."
Yesterday in Norfolk and Waveney there continued to be high demand for fuel and long queues outside petrol stations, especially in Norwich during rush-hour.
However, there were fewer reports of places running out and the picture was a little more promising outside of the city.
Despite the assurances, Steve McNamara, general secretary of the Licensed Taxi Drivers Association in London, said there was little sign of the situation improving on the ground.
Retail fashion giant Next said shortages would continue to plague the wider economy in the run-up to Christmas unless the Government took action to address the "looming skills crisis", stating the shortage of HGV drivers had been "widely predicted for many months" and for immigration rules to be relaxed to avoid further shortfalls.
The call came as figures from the Department for Transport revealed a backlog of more than 56,000 applications for vocational driving licences, including HGV and bus, permits waiting to be processed.
Boris Johnson said on Tuesday that measures were being put in to ensure "all parts of our supply chain", not just petrol, were able to "get through to Christmas and beyond".
In Norfolk, garage owners have said that they have seen this level of demand before, but never to this level, with heated arguments breaking out as panic buying reached its peak.
Police have urged the public not to call them over queues for traffic and have asked drivers to consider whether it is necessary to create congestion on roads.
Norfolk Fire and Rescue have asked people not to stockpile petrol at home as it can be "extremely dangerous".
Schools in the county have seen some pupils who rely on special school transport arrangements unable to attend school.
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