Paul Urey, 45, died in captivity on Sunday, according to the human rights ombudsperson for the Moscow-supported leadership in Donetsk.
His mother Linda Urey expressed her anger, branding the separatists “murderers”, and asking: “Why did you let him die?”
Russian ambassador to the UK Andrei Kelin was summoned to the Foreign Office to face questioning over what happened to Mr Urey, who was detained near the Ukrainian city of Zaporizhzhia in April.
Daria Morozova, the ombudsperson, branded Mr Urey a “mercenary” and claimed he 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.
Ms Truss said she was “shocked” by reports of Mr Urey’s death.
In a statement, the Foreign Secretary said: “Russia must bear the full responsibility for this.
“Paul Urey was captured while undertaking humanitarian work. He was in Ukraine to try and help the Ukrainian people in the face of the unprovoked Russian invasion.
“The Russian government and its proxies are continuing to commit atrocities. Those responsible will be held to accountable. My thoughts are with Mr Urey’s family and friends at this horrendous time.”
Sir Tim Barrow, the second permanent secretary at the Foreign Office, was to urge Mr Kelin to clarify the status of Mr Urey and demand that Russia meets its obligations under international humanitarian law.
Pauls mother, Ms Urey said she is “truly angry” in a post on Facebook.
She said her son had been taken from her at birth and, after finding her, he had been taken from her again.
“Cruel cruel world,” she added.
Speaking at the time of his capture, Ms Urey told Sky News she had begged her son not to go to Ukraine.
She added: “He said, ‘Muma I can’t live with myself knowing people … need help to get to a safe place, I have to go. I would feel bad’.”
In April, the Presidium Network, a non-profit group, said Mr Urey and fellow Briton Dylan Healey had been captured at a checkpoint south of the city in south-east Ukraine.
Mr Urey, who was born in 1977 and was 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.
The Presidium Network said it was concerned that Russian forces might think the men were British spies.
A No 10 spokesman said the Foreign Office is “urgently investigating” the “clearly alarming reports”.
“Our thoughts are obviously with his family and friends,” he added.