Vice News's Jake Hanrahan and Philip Pendlebury, and Iraqi Mohammed Ismael Rasool, were detained in Diyarbakir, south-east Turkey on Thursday.
Vice News said they had been moved to a "high security prison" five hours away.
Police reportedly questioned them about alleged links to Islamic State and Kurdish militants, charges they deny.
Vice News has condemned the charges as "ridiculous", and a "baseless" attempt by the Turkish authorities to censor their coverage.
The group had been filming clashes between police and youths from the outlawed Kurdistan Workers' Party (PKK) which have erupted in recent weeks, the organisation said.
Turkey has limited journalists' access to the region.
A Foreign Office spokesman said it was "concerned" about the arrests, and expected Turkey to uphold EU obligations to protect press freedom.
"Respect for freedom of expression and the right of media to operate without restriction are fundamental in any democratic society," he said.
As a state part to the European Convention on Human Rights and UN Declaration of Human Rights, "we would expect the Turkish authorities to uphold the obligations enshrined in those agreements", he said.
Consular officials were in contact with the group, he added.
A lawyer for the group told the BBC they had been detained by police in their hotel, and their cameras and computers had been confiscated.
They were formally charged by a Turkish court with "working on behalf of a terrorist organisation" on Monday. They have denied all charges.
They have until next week to lodge an appeal, but their lawyer said he was "not optimistic" about securing their release.
Kevin Sutcliffe, Vice's head of news programming in Europe, said they had now been transported to a prison facility more than five hours away from where their legal representation was based, and from the court where they are due to appear.
"This move appears to be a blatant obstruction of the fair legal process that Turkey has repeatedly pledged to uphold," he said.
Vice News said all three men were experienced reporters and had worked extensively abroad.
Mr Hanrahan, from Northampton, and Mr Pendlebury, from Wigan, had worked together on numerous stories, including the migrant crisis in Calais, it said.
Journalist and translator Mr Rasool, who was born in Iraq and is based in Turkey, has worked extensively in the Middle East with the Associated Press, Anatolia Agency, and Al Jazeera, it said.
No further court dates have yet been set.

Northumberland County Council is planning to scrap Haydon Bridge station as well as downsizing West Harton Community Station.
Dave Ledger, chairman of the Northumberland Fire and Rescue Authority, said the council had "no choice" but to make the cuts.
The council also plans to scrap engines in Ponteland, Seahouses and Wooler and replace them with smaller appliances.
It has to save £500,000 on top of £1.5m cuts and has just finished a three-month consultation on its proposals.
The authority said a number of concerns had been raised, including how the county would cope in the face of further flooding when fire crews are called to help.
During the consultation it received three petitions, 84 online responses and 76 letters raising concerns over the plans, a spokesman said.
Mr Ledger, who is also the deputy Labour leader of Northumberland County Council, said: "To say I am concerned about the future is an understatement.
"We simply have no choice. The Government keeps saying we have choices - well I'd like them to tell us what the choices are."
The fire service has 88 full-time firefighters and 180 on-call officers in the county.
A full cabinet meeting will be held on 21 March when a final decision will be made.
Mr Ledger added: "Should the recommendation be approved, we will continue to have 21 emergency response vehicles and, through the introduction of smaller fire appliances, in some areas we will be able to increase the cover we provide."
The Foreign Office has said it is "concerned" about the arrest of two UK journalists and their fixer in Turkey, accused of helping a terrorist group.
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A fire station in Northumberland is facing closure amid £500k budget cuts.