A broadcast journalist said she was handcuffed and in police custody for five hours after being arrested while reporting on a Just Stop Oil protest.
LBC reporter Charlotte Lynch said she was on a road bridge over the M25 in Hertfordshire on Tuesday.
She said she was arrested on suspicion of conspiracy to commit a public nuisance, before being released.
The spokesman for Rishi Sunak said the prime minister believed it was "vital journalists are able to do their job".
Hertfordshire's Chief Constable Charlie Hall said measures were now in place so legitimate media could carry out their reporting.
He added that they had made a request for another force to independently investigate Hertfordshire Police's approach to the protests.
Ms Lynch said the incident was "absolutely terrifying".
It comes after a photographer and a filmmaker said they were held in police custody for about 13 hours after being arrested while trying to cover the protests earlier this week.
Wednesday has seen a third consecutive day of protests taking place around the London orbital motorway.
Just Stop Oil said it was calling for the government to tackle climate change by ending the country's use of fossil fuels, to invest in renewable energy and for better building insulation.
The LBC reporter said her arrest happened on a bridge between junction 20 (Abbots Langley) and junction 21 (M1/St Albans interchange).
She said she showed officers her press card and explained she was reporting on the demonstration, but her phone was taken and she was arrested.
Ms Lynch said she was searched at the side of the road, before officers seized her devices and took her to Stevenage police station in a custody van.
She said: "That journey took over an hour because of the M25 being closed.
"I was in the back of a police van, my hands were in front of me, handcuffed the entire time, on my own, the two police officers were behind the glass cage.
"That's when it dawned on me 'gosh, I could be charged here' and everything runs through your mind 'have I actually committed this offence?' even though I knew I hadn't.
"We got to the police station and I thought I'll answer their questions and I'll be on my way."
Ms Lynch said officers wanted to know how she knew about the protest.
She added that she was detained in a cell for five hours before being released with no further action.
"I just burst into tears," she said. "I just couldn't believe where I was. I felt like a criminal.
"It was absolutely terrifying being in a cell with a pad for a bed in one corner and a metal toilet in the other.
"I was just doing my job. What's also terrifying is what this means for press freedom. It was blindingly obvious I was a reporter."
Dawn Alford, executive director of the Society of Editors, said she was "deeply concerned" by reports of the arrests.
"We strongly condemn the arrest of journalists in the course of their work and will be writing to Hertfordshire Police to seek an urgent explanation and seek assurances that its officers respect the rights of journalists and understand that such actions threaten press freedom," she said.
Mr Sunak's official spokesman said: "It's vital journalists are able to do their job freely without restriction.
"Operational decisions are a matter for the police but the prime minister strongly believes in championing press freedoms.
"We wouldn't want to see those freedoms impeded whilst journalists are going about their day-to-day business."
A statement from Hertfordshire Police said: "Our officers have been instructed to act as quickly as they can, using their professional judgment, to clear any possible protesters in order to get roads up and running and to prevent anyone from coming to harm.
"However, Chief Constable Charlie Hall recognises the concerns over the recent arrests of journalists who arrived at these locations and have been present with the protestors at the scenes.Â Additional measures are now in place to ensure that legitimate media are able to do their job.
"In addition, Mr Hall is today requesting an independent force to examine our approach to these arrests and to identify any learning we should take in managing theseÂ challenging situations."Â
The police and crime commissioner for Hertfordshire, David Lloyd, said: "I support the role of a responsible free press being an essential pillar of a democratic society.
"While I am not involved in operational matters, policing these incidents is a very challenging and complex task.
"I am speaking to the chief constable to obtain more information about the circumstances of this arrest, and others, to obtain the complete picture of what occurred."
The National Police Chiefs' Council chairman, Martin Hewitt, said officers were under pressure when dealing with protesters but media should not be prevented from reporting on them.
"There's an enormous amount of pressure... but, of course, there is a right for journalists to go and report on those occasions and that shouldn't be prevented in any way," he said.
Ms Lynch said she was "pleased" the arrest would be examined.
"I hope what I've gone through and the ordeal I've gone through means no other journalist has to go through it again," she said.
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