The Maritime and Coast Guard Agency said 81 people had taken to lifeboats and 30 remained aboard the vessel Athena fighting the fire. There were no reports of injuries.
Nearby commercial vessels were heading to the area, 230 miles (370 kilometers) southwest of the Scilly Isles, to rescue the crew, which includes Chinese, Russian, Peruvian and Scandinavian personnel.
A Royal Navy helicopter was on standby, but the ship might be too far out to sea for an airborne rescue, coast guards said.
The 344-foot (105 meter) fish-processing ship is managed by shipping company Thor and based in the Faeroe Islands.
The coast guard agency said the fire had subsided somewhat and the situation appeared to be under control, but that the crew members’ lives were still at risk.
“The guys are in life rafts bobbing on the ocean,” said the agency’s Fred Caygill. ( Associated Press )