But the Government's decision is unlikely to end a debate between historians about the justice meted out to the men, some of whom were in poor health and whose nerves were shattered by the experience of combat and shell-shock, not then recognised as a medical condition.
John Major said: 'I have reflected long and hard but I have reached the conclusion that we cannot rewrite history by substituting our latter-day judgement for that of contemporaries, whatever we might think.'
Andrew MacKinlay, Labour MP for Thurrock, who led the campaign to get the dead soldiers pardoned, said: 'The reverse is true. I'm not seeking to rewrite history. I'm seeking clarity and precision.' He added that Mr Major was the first Prime Minister to consider the matter since David Lloyd-George and had been most sympathetic.
Some next-of-kin were never officially notified. An order of September 1916 instructed that those executed should just have the word 'died' on their gravestones - not 'killed in action'. But families sometimes found out. For example, 10495 Private A Ingham, of the Manchester Regiment, 'died' on 1 December 1916. His family were entitled to add their message, for 1 1/2 d a letter. 'Shot at dawn,' his father put.
Historians have argued for years about the treatment of those convicted by capital Courts Martial during the largest and longest European land campaigns ever fought by the British Army. At the peak of the war on the Western Front, in August 1917, 2,044,627 British soldiers and officers were fighting, and about 5 million entered the Army during the 'War to end War'.
About 10 per cent of those sentenced to death were executed. The Government investigated the cases of 307 executed for cowardice, desertion and other infractions of military discipline. A further 37 were also executed for murder.
About 30 files in the Public Records Office, including some still closed to the public, were examined, Mr Major said. 'The files record each stage of the case, up to the final decision by the Commander-in-Chief (Field Marshal Douglas Haig). No evidence was found to lead us, including the Judge Advocate General, (the senior lawyer to the Army, Judge J W Rant QC) to think that the convictions were unsound.'
The view that many of those executed were victims of an unduly harsh system was put by Julian Sykes and Julian Putkowski in their 1989 book Shot at Dawn. Alan Bleasdale's play and television series The Monocled Mutineer (1986) reinforced the view of a pitiless military regime.
Judge Anthony Babington's For the Sake of Example (1983) also criticised the 'discipline of fear' but said that many of those executed were trouble-makers.
But Mr MacKinlay's campaign focused on those whose nerve or endurance broke. 'Even if I don't succeed in getting the Royal Prerogative exercised in favour of the 307 . . . they have been vindicated by the most important court in the land - British public opinion,' he said.
Mr MacKinlay highlighted the case of Private Harry Farr, aged 25, who was executed for cowardice at Ville-sur-Ancre in October 1916. Pte Farr was serving in the 1st Battalion West Yorkshire Regiment. He was suffering from shell-shock, returned to the front prematurely and then cracked, screaming 'I cannot stand it'.
His grand-daughter, Janet Booth, of Farnham, Surrey, said her grandmother, now 98, did not tell the family until recently that Pte Farr was executed for alleged cowardice. 'She has lived with the shame and humiliation all these years. I think, for her sake, a pardon would mean she could rest in peace that he was not a coward,' Mrs Booth said.
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