They are particularly concerned at the situation in rural areas where shoppers may not have public transport access to find the products they need.
Northumberland Labour says the problem is partially down to the impact of Brexit and the resulting shortage of lorry drivers, not just Covid-19.
Leader Scott Dickinson said: “Whatever side you were on in the Brexit debate, there’s no doubt that now we’re dealing with after effects.
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“Whether it’s a shortage of people to join the NHS or critical other public services or pick fruit and vegetables, work in hospitality or, in this case drive lorries to deliver vital food, it just goes to show what an absolute shambles the whole thing is.
“Through our council leaders and through Labour at a national level we will be pressing the government to explain why this situation has developed and what they’re planning to do about it.
“It’s just not good enough.”