The bodies had been buried by local people when they were washed up on the northern Russian shore following the disappearance of the Hull-based ship in 1974.
The graves were opened on Friday so that the scientists could take DNA samples from the bodies. Two more bodies, exhumed yesterday from graves thought to contain crew members, turned out to be women.
The Gaul sank off northern Norway in February 1974, with the loss of all 36 crew, amid rumours it had been involved in a secret spying mission.
According to a spokeswoman for the Department of the Environment, Transport and the Regions, the scientists have now completed their mission to Russia and will issue a report on the findings later this year. "The team have now followed up all the leads they can," she said.
The scientists will take the DNA samples to laboratories in Wetherby, West Yorkshire, where they will be compared to those taken from relatives of the crew.
The operation, which was described as "difficult and sensitive" by Deputy Prime Minister John Prescott, is designed to ease the uncertainty for the families of those who died.
The Gaul disappeared without a distress message and the only wreckage recovered was a small buoy, leading to speculation that it had been spying on the Russian navy.
An investigation in 1974 concluded that the trawler had capsized and foundered in heavy seas.
And a second report in 1999, carried out by the Marine Accident Investigation Branch after the wreck was discovered in 1997, found no evidence of espionage, confirming that the vessel was sunk after being pounded by large waves.
On publication of the report, Mr Prescott announced that he was reopening the formal investigation into the sinking.Reuse content