Dr Abbas Khan, an orthopaedic surgeon from Streatham, south London, travelled to the city of Aleppo last year to help civilians.
His brother Afroze said the Syrian National Security Agency had promised his release this week but yesterday it said he had died, BBC reported.
"My brother was going to be released at the end of the week. We were given assurance by the Syrian government. My brother knew that. He was ready to come back home. He was happy and looking forward to being released," Afroze was quoted as saying by BBC.
A spokesperson for the Foreign Office was quoted as saying, "We are extremely concerned by reports that a British national has died in detention in Syria."
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Abbas, who was married with two young children, spent a year training as a surgical registrar in Carlisle and also worked at the Royal National Orthopaedic Hospital, a report in The Times said.
He had been volunteering with Human Aid, a charity, during a six-month sabbatical from Epsom and St Helier University Hospitals NHS Trust, when he went missing, it said.
He was transferred to better conditions in a prison outside Damascus, where his mother - a British-Indian - has spent the past four months begging Syrian bureaucrats for his release, the report said.
"I have kissed the shoes of so many officials," Fatima Khan, 57, was quoted as saying.
Another brother of Abbas, Shahnawaz Khan, also a doctor, has said that the family had little choice but to attribute the lack of progress in securing his release to the fact he is a Muslim of Indian descent.