The Foreign Office says it condemns the exploitation of prisoners of war and civilians for political purposes.
It's after Russian state media claimed two more British men have been charged with carrying out mercenary activities by a Moscow-backed separatist region in Ukraine.
Aid worker Dylan Healy and military volunteer Andrew Hill are believed to be held in the self-styled Donetsk People’s Republic - according to the Russian news agency Tass.
However, there's been no independent verification of the charges.
The Foreign, Commonwealth and Development Office (FCDO) is understood to be actively investigating and is providing support to the men’s families.
A view shows a destroyed anti-tank gun MT-12 "Rapira" during Ukraine-Russia conflict in the city of Sievierodonetsk in the Luhansk Region, Ukraine June 30 Alexander Ermochenko
An FCDO spokeswoman said: “We condemn the exploitation of prisoners of war and civilians for political purposes and have raised this with Russia.
“We are in constant contact with the government of Ukraine on their cases and are fully supportive of Ukraine in its efforts to get them released.”
It comes after a video shown on Russian television in April featured a man speaking with an English accent who appeared to give his name as Andrew Hill from Plymouth.
A pro-Kremlin website said Mr Healy and Mr Hill would face the same mercenary charges as Aiden Aslin and Shaun Pinner, two British military volunteers captured in Mariupol who have been condemned to death in Donetsk.
The European Court of Human Rights (ECtHR) on Thursday intervened in the case of Mr Aslin and Mr Pinner.
The Strasbourg-based court indicated to Moscow that it should ensure the death penalty imposed on Mr Aslin, 28, originally from Newark in Nottinghamshire, and Mr Pinner, 48, from Bedfordshire, is not carried out.
Mr Aslin and Mr Pinner were living in Ukraine before the invasion and the UK Government has insisted that, as legitimate members of the Ukrainian armed forces, they should be treated as prisoners of war under the Geneva Convention.
Russian President Vladimir Putin addresses participants of the IX Forum of Regions of Russia and Belarus, via video link in Moscow, Russia July 1 Mikhail Metzel
Responding to the reports about Mr Healy and Mr Hill, Kristyan Benedict, Amnesty International UK’s crisis response manager, said: “As with Aiden Aslin, Shaun Pinner and Saaudun Brahim, this is a sham process designed to exert diplomatic pressure on the UK, not least as it comes shortly after Britain announced a large shipment of weapons for Ukraine.
“Under the Geneva Conventions, captured combatants and other protected persons should be humanely treated at all times.
“In exploiting their capture of Dylan Healy and Andrew Hill like this, Russia and its proxies in the Donetsk People’s Republic are already adding to a huge catalogue of war crimes they’re committing in this war.
“The chances of Healy and Hill receiving a fair trial in either the Donetsk People’s Republic or in Russia itself are vanishingly small.
“Unless the authorities present clear evidence that Healy and Hill are implicated in war crimes, this sham judicial process should be halted immediately.”
On Wednesday the Government announced it was imposing sanctions on Russia’s second richest man, Vladimir Potanin, and Vladimir Putin’s cousin, Anna Tsivileva, in the latest round of measures targeting allies of the Russian leader.
Mr Potanin is the owner of the Interross conglomerate.
Ms Tsivileva is president of the JSC Kolmar Group coal mining company.