Police are refusing to speak to Motorcycle News after its chief reporter asked a spokeswoman a question 36 times and broadcast the audio interview online.
The row has broken out after MCN reporter Steve Farrell asked a South Yorkshire police press officer why a speed camera staff member resigned after a criminal inquiry.
Farrell asked the spokeswoman 36 times why she could not give him any more information about the resignation. The telephone recording was published online by MCN.
The Association of Chief Police Officers responded last Friday by advising all of its staff not to speak to the newspaper, accusing it of making a "covert and undisclosed recording".
A spokeswoman for ACPO said: "I can confirm that a note has been sent from ACPO to all chief constables, suggesting their staff refrain from engaging with MCN while legal advice is being sought regarding the covert and undisclosed recording of police staff."
MCN news editor Tom Carter told Press Gazette: "The recording was made in a full and frank way.
"It was a journalist asking a question of a press officer and we felt the fact she refused to answer the question 36 times without giving any reasonable explanation was out of order."
In a typical exchange in the nineminute recording, Farrell asked: "What I'm asking you is why you won't tell us anything else?" to which the spokeswoman replied: "I'm just relaying an answer to your question."
MCN picked up the story from local news reports which claimed there had been a "non-enforcement" of a speeding penalty against a relative of the speed camera staff member — prompting the criminal inquiry and resignation.
MCN has been running a two-year campaign to demand "less reliance on speed camera technology" and more police officers on the road to protect vulnerable road users.
Carter added: "Rather than give our readers half a story, to be put off that many times by a press officer from the South Yorkshire police department, we felt it was perfectly within our rights and the rights of our readers to understand the comments that were made to what would be a perfectly reasonable question."