UK supermarkets could see food shortages at Christmas due to Brexit-related supply chain disruption, the chairman of Tesco has warned.

John Allan, who has overseen the country’s largest grocer since 2015, said the Government should change rules for lorry drivers to allow for more emergency workers from overseas to help solve the problem.

Retailers and restaurants chains, including Nando’s and McDonald’s, have been hit by product shortages as meat packers and other manufacturers have also faced significant worker shortages.

Mr Allan told BBC Radio 4’s World at One that supermarkets would normally be building stock now ahead of Christmas and that the “straightforward solution” to driver shortages would be “to allow UK industry to bring in skilled drivers from elsewhere”.

He added: “We are very short of drivers, it’s a combination of many EU drivers having decided to go home and also the ageing age-profile.

“I think certainly Brexit has been a contributor to that but also improving economies, higher wages in some of the countries that they’ve come from historically, have also led to that flow.”

He said there could be some shortages as a result but stressed it is important not to “over-dramatise” the extent of the issue yet.

He said: “At the moment we’re running very hard just to keep on top of the existing demand and there isn’t the capacity to build stocks that we’d like to see. So, in that sense, I think there may be some shortages at Christmas.

“But, again, I wouldn’t want to over-dramatise the extent to which that would be the case, I think it’s very easy to make a drama out of a modest crisis.”

Iceland managing director Richard Walker also warned the UK faces “big shortages” of lorry drivers, with the situation threatening Christmas products.

“Of course, we’ve got Christmas around the corner, and in retail we start to stockbuild really from September onwards for what is a hugely important time of year,” he said.

“We’ve got a lot of goods to transport between now and Christmas, and a strong supply chain is vital for everyone.

“The reason for sounding the alarm now is that we’ve already had one Christmas cancelled at the last minute. I’d hate this one to be problematic as well.”

Mr Walker added the chain has seen daily delivery cancellations as the disruption continues.

“We’ve had deliveries cancelled for the first time since the pandemic began, about 30 to 40 deliveries a day,” he said.

The retailer said it has seen particular lines, such as bread and soft drinks, impacted by issues facing suppliers.

Steve Murrells, chief executive of the Co-operative Group, warned that current food shortages are at a “worse level” than he has ever seen, with the company having to reduce product range to help serve customers.

He told the Times newspaper: “The shortages are at a worse level than at any time I have seen.”

Mr Murrells said the disruption to supply has been driven by “Brexit and issues caused by Covid”, and the firm is retraining staff as lorry drivers to help fill vacant roles.

Road haulage bosses have said there is a shortfall of around 100,000 drivers, partly caused by the exit from the UK during the pandemic of thousands of EU drivers who have not yet returned.

Industry groups have also said training for new drivers is taking months, making the shortfall in numbers difficult to resolve quickly.

Labour shortages, which have also affected meat packing and fruit picking jobs, have caused shops and fast-food restaurants to struggle for stock.

Subway and McDonald’s are some of the latest victims of the shortages.

Sandwich shop chain Subway said it has seen “minor supply chain shortages” but stressed it has ensured that disruption to customers is minimal.

Meanwhile, McDonald’s ran out of milkshakes in most of its UK restaurants due to the ongoing supply problems.

The burger chain has also been left without bottled drinks across its 1,250 outlets in England, Scotland and Wales as the lorry driver shortage takes its toll.

A spokesman said the group is “working hard to return these items to the menu”.

It comes a week after restaurant chain Nando’s shut almost 50 restaurants because of reduced chicken supplies.