Retailers say it is up to the police to enforce rules on face coverings in shops, as the government seeks to encourage mask wearing in a broader range of settings.
However, the police say they will only step in as a last resort.
The stand-off comes as representatives of both groups met government officials on Wednesday to explore how to improve compliance.
Masks are mandatory in most indoor public settings including shops.
The rules have recently been extended to include taxis and minicabs, for customers entering bars, cafes and restaurants, and for hospitality and retail staff.
The government said the meeting was to explore “opportunities for collaboration” between law enforcers and retailers.
However, the British Retail Consortium said its members, who include the large supermarket chains, did not feel they could be held responsible for the small minority of shoppers who refuse to wear a mask.
“The government has decided that the responsibility for enforcing the law about individuals wearing face coverings is for the police, not retailers, and we welcome their support,” said Tom Ironside, director of business and regulation at the BRC.
At the same time the National Police Chiefs Council confirmed it expects retailers “to manage entry to their stores and compliance with the law while customers are inside”. The NPCC said police officers would only be involved “as a last resort”.
In England, the police can issue a £200 fine to anyone breaking face covering rules. In Scotland, Northern Ireland and Wales, a £60 fine can be imposed. Repeat offenders face bigger fines.
NPCC figures show 89 fines were handed out across England and Wales between 15 June and 21 September for non-compliance.
Shops are legally obliged to ensure customers know the rules around face coverings. Most display prominent signs reminding customers of the rules, and some have staff speaking directly to customers at the door.
Only a very small number of shoppers refuse to cover their faces according to figures from the Office for National Statistics, which found in August almost 96% of adults wore a mask in some settings outside the home.
However, heated debates on social media suggest there is a strong degree of polarisation between those who believe face covering rules to be an infringement of their personal freedom and those who view refusing to wear one as selfish and dangerous.
The trade union representing shopworkers, Usdaw, said if staff were asked to confront non-compliant shoppers it could create “a major flashpoint for abuse, threats and violence”.
“We’ve been very clear from the beginning it’s not the responsibility of shop workers to enforce this,” said Usdaw spokesman David Williams.
“This is the personal responsibility of shoppers. As long as they know face coverings are mandatory in shops, it’s their decision if they choose to ignore it.”
Moreover, some members of the public are legitimately exempt from mask-wearing for medical reasons and it wasn’t appropriate for staff to ask shoppers to share private medical information, he said.