"The post-mortem is either concluded or very near to conclusion, Nabeel Sheikh, senior partner of Neumans law firm, told AFP yesterday.
"I think the decision will probably come tomorrow (Tuesday) or just after Boxing Day (Thursday)," he added.
The results of the autopsy, carried out at the Queen's Hospital in east London, will be passed to the coroner, who will decide if the results are suspicious enough to warrant a formal inquest.
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.
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Doctor Nat Carey, one of the Britain's best-known forensic pathologists, was asked by the family to participate in the post-mortem, along with a pathologist from Britain's interior ministry.
The Metropolitan Police's counter-terrorist command also "afforded its assistance for the post-mortem to be conducted as effectively as possible," explained Sheikh.
The lawyer on Sunday told AFP that pathologists would be looking for signs of torture on the body.
"The family hopes that all relevant tests as deemed necessary are carried out so as to ensure the post-mortem is concluded without delay and the body laid to rest as soon as possible," Sheikh said.
British Prime Minister David Cameron has written to the doctor's mother, saying Damascus must answer for his "sickening" death, Sheikh revealed Sunday.