Syria claims Abbas Khan, who was arrested last year after travelling to Aleppo to treat wounded civilians, committed suicide. But a British minister said this week that he was "in effect murdered" by the regime.
A British government source confirmed that Cameron had written to Khan's family.
It is understood that he wrote: "Abbas's death is a sickening and appalling tragedy and it is right that the Syrian regime should answer for it."
The body of the 32-year-old orthopaedic surgeon was flown back to London from Beirut today. An autopsy will be conducted to determine how he died.
The family's lawyer, Nabeel Sheikh, said relatives were "relieved that his body has been repatriated" and that the body was being transferred to a coroner's court in east London, where tests would be carried out.
Sheikh told AFP that pathologists would be looking for signs of torture on the body.