A staff member tested positive for coronavirus, but filming continued until another test came back negative, according to reports.
Crews members claimed that filming carried on for a few hours after the first test, until the production was halted when another staff member discovered what had happened.
Bectu, a union for workers in the media and entertainment industry, said filming should have stopped immediately.
Spencer MacDonald, one of the union's national secretaries, told The Guardian: "The safety protocols are in place to create a safe working environment for cast and crew.
"Therefore the production should have informed everyone immediately and stopped filming.
"Otherwise a lapse like this could have contributed towards the spread of the virus.
"We are currently waiting for the production to respond."
This latest series, currently in production, is due to be the sixth and final one.
A spokesman for the show said: "Filming was stood down on Peaky Blinders because of a false positive test result for a member of the crew.
"In line with protocol, this person took an NHS test and anyone who came into contact with them self-isolated – the safety of our team on Peaky Blinders is of paramount importance.
"The NHS test came back negative and filming resumed on Thursday."