Assurances from Tesco that they have “have good availability of fuel” failed to stop queues forming at some of their pumps today.
At Hampton, Peterborough, queues of drivers were trying to get in to re-fill their tanks.
Tesco insists they have “deliveries arriving at our petrol filling stations across the UK every day”.
But people are voting with their steering wheels and heading to the pump.
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This week Tesco warned the Government that it has a shortfall of 800 drivers and is concerned about panic buying in the run up to Christmas if the nationwide HGV crisis is not addressed.
The UK's largest supermarket also called on the Government to temporarily make it easier to bring in workers from abroad to ease the issue.
The warning, which was first reported by ITV News, came in a meeting organised by the Cabinet Office.
Andrew Woolfenden, Tesco's UK distribution and fulfilment director, said it has only managed to attract as many drivers as it has lost to rival businesses over the summer despite offering £1,000 recruitment bonuses since July.
The Road Haulage Association has warned that there is a shortage of around 100,000 drivers across the UK, which has particularly impacted the food and drink supply chain.
Mr Woolfenden said the problem was industry-wide and described attempts by companies to recruit from the same, limited pool of drivers as like "moving deckchairs around".
On the call, he added: "Our concern is that the pictures of empty shelves will get ten times worse by Christmas and then we'll get panic-buying."
Meanwhile, Katherine Mercer, Amazon's public policy manager for the UK and Ireland, told the meeting that recruitment efforts were "back at square one" and that Christmas will be "a real challenge".
A Tesco spokesperson said: "While the industry-wide shortage of HGV drivers has led to some distribution challenges, we're working hard to address these and to plan for the months ahead, so that customers can get everything they need."
A spokesperson for Amazon said: "The festive season is always our busiest time of the year and, as we do every year, we'll be working to provide the best possible service for our customers."
A Government spokesperson said: "We recognise business is facing a range of challenges and we are taking steps to support them, including streamlining the process for new HGV drivers and increasing the number of driving tests.
"Progress has already being made in testing and hiring, with improving pay, working conditions and diversity.
"We are closely monitoring labour supply and working with sector leaders to understand how we can best ease particular pinch points."
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