Daria Morozova, the human rights ombudsperson for the Moscow-backed separatist leadership in Donetsk, said Paul Urey died in captivity on Sunday of chronic illnesses and stress.
“From our side, he was given the necessary medical assistance despite the grave crimes he committed,” she added.
A No 10 spokesman said the Foreign Office is “urgently investigating” the “clearly alarming reports”.
BREAKING. British volunteer Paul Urey "has died" in prison in Donetsk due to "chronic illnesses", Donbas pro-Russian separatists announce.
— Antonello Guerrera (@antoguerrera) July 15, 2022
“Our thoughts are obviously with his family and friends,” he added.
In April, the Presidium Network, a non-profit group, said Mr Urey and Dylan Healey were captured at a checkpoint south of the city of Zaporizhzhia in south-east Ukraine.
Mr Urey, who was born in 1977 and from Manchester, and Mr Healey, born in 2000 and from Cambridgeshire, travelled to Ukraine of their own accord, the organisation said.
They were not working for the Presidium Network, which helps to get aid into Kyiv.
The organisation said the pair went missing while driving to help a woman and two children evacuate.
The Presidium Network said it was concerned Russian forces may think the men are British spies.
The Foreign Office has said it is urgently seeking clarity about the situation.
A Foreign, Commonwealth and Development Office spokesperson said: “We are urgently seeking clarification from the Russian government on media reports that a British aid worker has died in Ukraine.”
Mr Urey’s appeared to confirm reports of her son’s death as she posted a series of messages on Facebook on Friday afternoon.
“Absolutely devastated,” Linda Urey wrote.
In a second post, she wrote: “I’m truly angry I told you he was a very sick man, I told he he was diabetic, I begged on sky news to give me my son back why did you let him die I want answers why didn’t you release him...”