The veteran, who raised more than £33 million for the NHS, was remembered at a private family service at Bedford Crematorium.
The prime minister will also join a "national clap" for Captain Tom Moore at 6pm.
“It just added a little bit more despair, misery and hurt onto what they were suffering as a family,” the Good Morning Britain host said.
The former footballer, who met Sir Tom last year, said he was “the very best of British”.
Captain Tom’s fundraising was laudable. But our NHS should never have to be a charity case, writes Harriet Williamson.
The centenarian was a beacon of hope in the fog of the first lockdown.
The Good Morning Britain presenters led the tributes following the war veteran and fundraiser's death at the age of 100.
Captain Tom Moore, who lifted the nation during the first stages of the coronavirus pandemic has died, aged 100. The centenarian raised over £30 million for the NHS, broke two Guinness world records, was knighted by Queen Elizabeth II and managed to have a number 1 song.
Sir Tom helped raised more than £32 million for the NHS by walking 100 laps of his garden before his 100th birthday in April.
Boris Johnson’s press secretary hits out, saying hospitalised veteran in PM’s thoughts “very frequently”.