Anyone alive who was convicted of consensual same-sex acts before the law was abolished can already apply to have their names cleared through the "disregard process", and will now receive an automatic pardon. Thousands of deceased people will also receive an automatic pardon.
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"It is hugely important that we pardon people convicted of historical sexual offences who would be innocent of any crime today," said Justice Minister Sam Gyimah.
"Through pardons and the existing disregard process we will meet our manifesto commitment to put right these wrongs."
Private homosexual acts between men aged over 21 were decriminalised in England and Wales in 1967, but the law was not changed in Scotland until 1980 and in Northern Ireland until 1982.
Turing was a computer scientist, philosopher and cryptologist who played a crucial role in breaking the Nazi Enigma code at Britain's Bletchley Park, which was recently dramatised on the big screen in "The Imitation Game".
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He was prosecuted for homosexuality in 1952 and forced to undergo chemical castration. He killed himself in 1954 at the age of 41. Turing was officially pardoned by Queen Elizabeth II in 2013, triggering calls for blanket pardons.
Liberal Democrat lord John Sharkey, who introduced the bill to clear Turing, said the latest government announcement heralded "a momentous day for thousands of families up and down the UK". "It is a wonderful thing that we have been able to build on the pardon granted to Alan Turing," he told the BBC.
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