The death of Paul Urey, 45, was confirmed by a British charity which described him as a humanitarian worker and denied he had any military background.
Urey was captured in southeast Ukraine in late April while attempting to help a woman who had been given permission to travel to the UK and leave Russian-controlled territory, said Presidium Network, a charity which had advised him on safety.
He was stopped at a checkpoint, detained and charged with "mercenary activities" by separatists in the DPR, a breakaway entity which is recognised only by Russia, Syria and North Korea.
Presidium Network said the UK's Foreign Office had informed Urey's family of his death.
A spokesperson for the Foreign Office told Reuters it was "urgently seeking clarification from the Russian government on media reports that a British aid worker has died in Ukraine".
Asked about Urey, a spokesman for Prime Minister Boris Johnson said: "They're clearly alarming reports and our thoughts are with his family and friends."
The UK's foreign office has summoned Russian ambassador Andrei Kelin to express "deep concern" over reports of Urey's death.
Daria Morozova, who has the title of human rights ombudsman in the DPR, said on social media that Urey had been suffering from diabetes and respiratory, kidney and cardiovascular issues.
"On our part, despite the severity of the alleged crime, Paul Urey was provided with appropriate medical assistance. However, given the diagnoses and stress, he passed away on July 10," she said.
Urey and another UK citizen, Dylan Healy, were detained at a checkpoint controlled by separatist forces in late April.
The co-founder of the Presidium Network, who was in touch with Urey before he was detained, said Urey had diabetes which needed to be treated with insulin injections.
"Without insulin and proper care, his life would have been in danger anyway," Dominik Byrne told Reuters.
The UK's Foreign Office and the Red Cross were able to carry out remote welfare checks on Urey by phone while he was in captivity but nobody beyond his captors had been in physical contact with him since late April, Byrne said.
There was no evidence Urey had a military background and that there was "no way" he was anywhere near "mercenary activities," as DPR officials allege, he added.
"They are really using these personnel as political pawns in this conflict - which is disgraceful" Byrne said of the Russian-backed separatists.
Two other UK citizens and a Moroccan man who were captured while fighting for Ukraine have been sentenced to death in the DPR for mercenary activities.
Two US citizens are also being held in the DPR and have not yet been charged.
Their families say the separatists are trying to secure a prisoner exchange and push the United States into official communications with the Russian proxies, something which could be seen as de facto recognition.
Urey's family are now calling on the DPR to release his body back to the UK, Byrne said.
The UK's foreign office has summoned Russian ambassador Andrei Kelin to express "deep concern" over reports of Urey's death.
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