More than three thousand people have signed a petition calling for Bicester Village to temporarily close after hundreds of people were pictured at the shopping complex.
Pictures on social media appear to show people struggling to maintain social distancing at the designer retail outlet in Bicester, Oxfordshire.
The petition is calling for it to be closed until changes are made.
Value Retail, which runs the complex, has been contacted for comment.
All shops in England are now allowed to open, but with strict safety measures.
Laura Wicks, who launched the petition, wrote she was “disgusted to see hundreds of people squashed into the street like Coronavirus never happened” and called for the complex to keep their staff safe.
The complex, which has 160 shops, said on its website visitors are temperature-scanned on arrival and they should keep a two-metre distance apart.
Shopper Adam Galbraith said keeping two metres was fine in the shops, but it was not being enforced “well enough” outside the shops at the luxury retail outlet.
Speaking to the BBC, he said: “It was definitely way too overcrowded to adhere to social distancing.
“For a complex of that size they should know how many people can be in this place safely and keep two metres distance, and that for me wasn’t monitored at all.
“What would have been better if they had the queues to get into the village outside, and gave customers a two-hour slot to do their shopping.”
He added queues outside the shops, which allocated a time to shoppers using an digital queuing app, were less busy.
Shopper Dr Tesh Amarasinghe said she had her temperature checked with a thermal scanner and social distancing within the stores was “excellent”, but she said there were difficulties maintaining the two-metre distancing in the outdoor walkways.
The GP, from Northampton, said: “It kind of took away the point of distancing in the shop, if you’re standing in a queue up to an hour really close [to others].”