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Nine of the crew of 32 are still missing.
The British ship Baltrover happened to be passing and was first to spot the collapse of the Sea Gem at 1409GMT.
It sent a radio message to shore for further help, and then picked up 19 survivors and two bodies from the sea.
The 5,600-ton steel barge had been converted into an oil rig comprising a drilling platform, living quarters and a helicopter landing pad.
It was supported on 10 steel legs 50 feet (15 metres) above the waves.
Two of these legs gave way as it was being prepared to move to a new location, and then the whole rig tilted sideways and sunk.
Men were seen jumping into the freezing cold sea - stained red with fuel - and clinging onto wreckage.
Survivors were brought ashore to Hull tonight.
They had been rescued in a joint effort by passing ships and two helicopters - one RAF and the other civilian.
Rescuers on the Leconfield-based RAF helicopter, which rescued three men, said that by the time they had arrived only one leg of the converted barge was left visible.
Flight Sergeant John Reeson described the horrendous conditions as he had tried to save them.
"We went out through a snowstorm," he said.
"It was clear weather around the oil rig but it was rough. There were waves 15ft to 20ft high. I went down the winch line to men I could see in the water. It was freezing cold. They had been in the water an hour or two before we got there.
"One man hanging on to a life raft clutched me with a grip of iron when I reached him. It was almost impossible to pick him up, but I managed it. He was desperate."
One of the rig workers, Robert Hessey, said the structure collapsed without any warning.
"I saw the crane topple over the deck," he said. "There was a loud sound of grinding and rumbling. I hadn't realised what was happening until I heard someone shouting, 'She's sinking.'"
Last September, after much public anticipation, British Petroleum's rig was the first to discover natural gas in the British sector 42 miles (67km) off the Lincolnshire coast.
Earlier this month Sea Gem also became the first rig to light a flare over the North Sea.
BP said the tragedy will delay its drilling programme. A new purpose-built rig, Sea Quest, is currently under construction in Belfast but it will be some months before it's ready to operate.
Altogether, 13 men lost their lives and five were injured.
Rescuers on the single RAF helicopter were honoured for their bravery in May 1966.
Flight Sergeant John Reeson, the RAF winchman, was awarded the George Medal. The navigator, Flight Lieutenant John Hill received the Air Force Cross and the pilot, Sergeant Leon Smith, got the Queen's Commendation.
A public inquiry into the sinking of the Sea Gem concluded metal fatigue in part of the suspension system linking the hull to the legs was to blame.
The inquiry recommended improving safety precautions such as regular inspections, a clear chain of command and better communication with workers
The Sea Gem's well was written off and new wells were drilled in Block 48/6 area, now known as West Sole Field.
The new Sea Quest floating platform began drilling nearby in July 1966.
The dangers of extracting oil at sea was further underlined in 1988 with the tragic accident of the Piper Alpha platform.
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