Posting on the 95-year-old’s Twitter account, his son John said: “At 3:39 this morning, my dad Harry Leslie Smith died. I am an orphan. #istandwithharry.”
His family said last week he had become “critically ill” in Canada hours before he was due to fly back to the UK.
After announcing his death, his son tweeted: “My dad had been so dreadfully thirsty because he’d had nil by mouth orders for almost a week. So when he decided that the potential for full recovery was not possible, he was allowed to drink a beer. Sadly though he couldn’t eat.”
Mr Smith became a prominent figure after his address to the 2015 Labour conference, moving many to tears with his recollections of life and death in the UK before the existence of the NHS.
He was brought up in poverty in Yorkshire, where his father had been a coal miner, but struggled to find work. As a child Mr Smith helped support the family selling beer from a cart, but they were frequently forced into the workhouse.
His sister died when she was 10 years old from tuberculosis, with the family unable to afford a doctor.
Mr Smith joined the RAF in 1941 and spent several years in Germany as part of the Allied occupation force. He met his wife Friede during the posting and after the war the couple returned to Yorkshire before emigrating to Canada in the 1950s.
His early experiences were a key source of motivation for his writing.
“We must never ever let the NHS free from our grasp because if we do your future will be my past,” he said.
Jeremy Corbyn has led tributes to Mr Smith, saying “We will all miss Harry Leslie Smith – he was one of the giants whose shoulders we stand on.
“A World War Two veteran who dedicated his life to fighting for our National Health Service, a peaceful world and for countries to meet their moral responsibility by welcoming refugees.”
Deputy Labour leader Tom Watson said: “Harry Leslie Smith will remain an inspiration to all in the Labour movement engaged in the fight for justice and fairness. The world is a far better place for his life, words and deeds; and a far sadder place with his loss. Farewell @Harryslaststand.
Speaking to The Independent last week, his son said from the hospital: “I think what anyone can learn from Harry is you don’t have to be silent in a world gone mad. You can speak up and if your voice is honest and true it will be heard.”
He said his father was “just an ordinary man who wouldn’t allow his past to be forgotten so that history could repeat. He wants the suffering of his generation to be a warning to others not to allow populism or right wing politics to erode the progress the Social Welfare State has given to ordinary folk.”
Mr Smith began writing after the death of his wife.
He was a prolific Twitter user and the author of several books about post-war Britain including Harry’s Last Stand, Love Among the Ruins and Don’t Let My Past Be Your Future, and his son said he wants to find a publisher for two self-published works detailing Mr Smith’s early life.
In his nineties, Mr Smith also became known for his campaigning work to highlight difficulties faced by refugees, travelling to the Calais “Jungle” refugee camp and encouraging the British government to react to the refugee crisis in Europe and the Middle East.
His son has said he will follow in his father’s footsteps. “I will endeavour to finish his projects,” he wrote on Twitter.
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