The incident involved a soldier from the Parachute Regiment who is alleged to have shot an Argentine prisoner of war in cold blood on a clifftop after the battle for Mount Longdon.
The current nine-month-old Scotland Yard inquiry into allegations of Falklands atrocities began after Vincent Bramley, a former lance-corporal in 3 Para, alleged in his book Excursion to Hell that fellow paratroopers had executed Argentine prisoners after the battle.
The MoD has always insisted that before the book's publication there was no evidence to justify such an investigation.
However new information suggests that the MoD was aware as far back as 1982 of one of the most serious allegations made in the book - but failed to act.
David Clark, Labour's shadow defence spokesman, will table a parliamentary question tomorrow asking whether the MoD received a report about the incident, and if it did, what action, if any, it had taken.
According to the fresh evidence, Major Peter Dennison of 3 Para, who is now a Lieutenant- Colonel, arrested a Para - later sent back to Britain - following the clifftop shooting incident and filed a report to his seniors. It is understood that he kept a copy of the report.
Mr Bramley told the Independent on Sunday: 'I was sitting with Captain Mason, Major Dennison and others. Below us and to one side, about 80 metres away was a burial party.
'We heard a scream, 'Mama, Mama]', I heard a bang, and saw a man topple from the cliff . . . Dennison was up and gone, his eyes full of fury, he was over there immediately.
'I looked over, but Mason said to forget that, to go over the ridge and start looking for intelligence.'
Another Para officer, who did not want to be named, but is in contact with Lt-Col Dennison, said yesterday: 'He believes in hindsight he did the right thing.'
He confirmed that Lt-Col Dennison was aware of the alleged shooting and the person responsible. He said: 'The information was passed up the chain of command.
'He is a very shrewd man. He is very wise and a correct-acting person and he would have done what was morally required.'
The soldier who was allegedly involved in the killing is understood to still be serving in the Paras.
Mr Mason, who has since left the Army, wrote to the Parachute Regiment last year to complain about the shooting, according to Mr Bramley.
The existence of a letter from Mr Mason has been confirmed.
In February Mr Bramley met Lieutenant-Colonel David Parker, the Regimental Colonel of the Paras.
Mr Bramley said: 'Parker told me that Captain Mason had made an official written complaint to him . . . about the shooting, and that in it he had named the NCO who had killed the prisoner.'
Lt-Col Parker told the Independent on Sunday: 'The letter in question was passed to the police. Bramley, I may say, had no business whatsoever discussing this with you.'
Dr Clark, speaking for Labour, said: 'There should be no cover- up - the British Army has a fine record in the way it treats prisoners of war and if anyone has broken the rules they must be brought to book. I fully support the setting up of the Scotland Yard inquiry into the allegations and it is essential the MoD are fully open with them.'
A MoD spokesman said: 'We take any allegations of war crimes very seriously, which has already been demonstrated by the fact we handed the matter over to the Crown Prosecution Service and it is being investigated by the Metropolitan Police.'
The Ministry said on Friday that senior officials involved in the current inquiry had no knowledge of a report by Lt-Col Dennison, and that it was not possible in the time available to check the records fully.
Lt-Col Dennison and Mr Mason were not available for comment.
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