Tesco shoppers around the county say they have been turned away at doors and checkouts for entering stores with young children.
Customers have accused the supermarket giant of discrimination - claiming they have been told to 'leave their children outside' while they pick up essential items.
In many cases, they say no alternative childcare is available - leaving them with no choice but to carry their kids with them while schools are closed.
"’I went to my local supermarket with my four-year-old but the man on the door said I couldn't bring her in," shopper Sarah Nendick explained.
"I asked him what I was meant to do but he didn't have an answer. I just had to leave and now I don’t know how I will get food."
In other cases, staff are refusing to service customers at the tills.
It comes as supermarkets across the country have warned shoppers they could have to wait more than four weeks to have their items delivered, after many reached full capacity online a fortnight ago.
One Tesco customer told Mirror Money she was left in tears after being told to leave her children outside.
"I've been struggling to get the food I need for my four kids because some of the shelves are bare, we've not got much left," Laura Smith said.
"I left my 10 and 12 year old at home and took my two under six year olds with me to Tesco."
The mum said she queued up for 40 minutes to enter the store - only to be told she wouldn't be allowed in with them.
"I had queued for 40 minutes but when I reached the front, they refused to let me in because I had the kids. They told me to leave them outside whilst I did a run around. I was in tears. Luckily a neighbour I know joined the queue and watched the kids, but if she wasn't there, I'd have had to leave."
On twitter, campaign group Pregnant then Screwed raised the issue with the supermarket.
"Dear @[email protected] we are receiving calls and complaints from single mums who have been told they can’t enter your supermarket with their children. As they are single mums they have no other option. Could you clarify your policy please?" the message read.
However, Tesco did not reply.
Another campaign group, the Single Mum's Business Network, said the grocer is effectively discriminating against single parents.
"It's heartbreaking," founder Julie Hawkins said.
"We've had parents get in touch after being told they shouldn't be shopping with their child - but what about single parents? Right now people are struggling with childcare, no one can get an online delivery and families need food.
"One mum told me she explained to the Tesco employee that she is a single mum. His response wasn't very sympathetic. She said 'what am I supposed to do? I can't come shopping on my own' to which he responded 'these are the rules. Sorry I cannot serve you.' Tesco then refused to let her pay.
"It makes sense to introduce limits for efficiency, but some of these people are single mums, dads, NHS workers - and they are all being turned away because they have no childcare."
Joeli Brearley, founder of Pregnant Then Screwed, added: "We have heard from a number of anxious single mothers who have been told to leave their children outside whilst they shop.
"Some have very young children, so leaving them in the car or in the house isn’t safe. They can’t leave them with their family due to social distancing, so what are they meant to do?"
"Online shopping is taking weeks to be delivered, so how are they meant to get food for their family. Social distancing is obviously hugely important, but leaving children outside supermarkets, is not the solution. This is an exceptionally stressful time for everyone, particularly single parents, who have likely lost their income due to childcare now that the schools are closed.
"This policing by supermarkets is now preventing them from buying food. It is wrong and it disproportionately impacts single parents who have no other solution."
Mirror Money put the claims to Tesco who have declined to provide an official statement.
However, it said it has not banned children from entering stores. The supermarket said it is encouraging people to shop with no more than one other person.