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The World War 2 veteran caught the public's imagination in April, just before his 100th birthday, when he was filmed doing laps with the help of a walking frame around his garden in the village of Marston Moretaine, north of London.
He hoped to raise 1000 pounds. Instead, he raised more than 30 million for the National Health Service, broke two Guinness world records, was knighted by Queen Elizabeth, scored a No. 1 single, wrote an autobiography and helped set up a charity.
"I wanted to update everybody that today ... my father was admitted to hospital," his daughter, Hannah Ingram-Moore, said on Twitter.
"Over the last few weeks he was being treated for pneumonia and last week tested positive for Covid-19. He was at home with us until today when he needed additional help with his breathing. He is being treated in a ward, although he is not in ICU (intensive care unit)," she said.
She said he had been receiving "remarkable" medical care in the past few weeks. The family knew the staff at Bedford Hospital would do all they could to make him comfortable and "hopefully return home as soon as possible", she added.
Britain has vaccinated nearly 9 million people against the coronavirus, with the over-80s in one of the top priority groups. But Sky News quoted a family representative as saying Moore had not yet received a vaccine because he was being treated for pneumonia.
His hospitalisation prompted an outpouring of support.
Prime Minister Boris Johnson said on Twitter his thoughts were with Moore and his family. "You've inspired the whole nation, and I know we are all wishing you a full recovery."
Opposition Labour leader Keir Starmer also wished him well, saying: "The whole nation hopes you get well soon @captaintommoore. You've been an inspiration to us all throughout this crisis."