The family were said to be “incredibly touched” and Hannah was seen to wipe away a tear during the emotional tribute.
There was also clapping at Premier League matches and at Bedford hospital, where he died from Covid on Tuesday, aged 100.
Troops took part outside the Army Foundation College in Harrogate, North Yorks — where Captain Tom was made an honorary colonel last year.
He had captured the country’s hearts by raising £39million for NHS Charities Together by walking laps of his garden.
There are now calls for a permanent memorial to Captain Tom — such as a statue or renaming a hospital.
Ahead of the applause, a minute’s silence had been held in the Commons to remember him and all who have died in the pandemic.
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Wessex Fire and Rescue clap for Captain Sir TomCredit: eddie mitchell
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People stand opposite the house of Captain Sir Tom Moore in Marston Moretaine in Bedforshire to pay tributeCredit: PA:Press Association
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Local residents join a national clap beside a mural of Captain Sir Tom Moore in East BelfastCredit: AP:Associated Press
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Doctors, nurses and health workers step out of the Chelsea and Westminster Hospital to clapCredit: AP:Associated Press
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Locals in Langport, Somerset, take to the streets to clap for Captain Sir TomCredit: Splash News
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Leicester City and Fulham players clap for Captain Sir TomCredit: Guardian News & Media / Free to use by all titles in perpetuity under NMC agreement
Echoing his catchphrase, PM Mr Johnson told MPs: “Captain Sir Tom Moore dedicated his life to serving his country and others.
“His was a long life, lived well whether during his time defending our nation, his time as an Army officer, or last year bringing the country together through his incredible fundraising drive for the NHS.
"As Captain Tom repeatedly reminded us, tomorrow will be a good day.
“He inspired the very best in us all and his legacy will continue to do so for generations to come.”
She said: “He was a light of inspiration at a time we have suffered a great deal individually and nationally over the last 12 months.
"He lifted the soul of the nation.”
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An NHS worker at Chelsea and Westminster Hospital in London claps for Captain Sir Tom MooreCredit: Reuters
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Locals join Captain Sir Tom's daughter Hannah Ingram-Moore, with her children Benjie and Georgia and husband Colin Ingram outside their house to pay tributeCredit: AFP or licensors
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Sir Lindsay Hoyle, Speaker of the House of Commons, and members of the house take part in the clap Credit: PA:Press Association
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Members of the Public and NHS staff at a Vaccine Hub in Newbridge, Wales paid tribute to Captain TomCredit: Getty Images - Getty
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A handwritten note left with flowers is seen near Captain Sir Tom Moore's houseCredit: Reuters
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The London Eye and buildings along the South Bank are lit up with the colours of the Union flag during a nationwide round of applauseCredit: PA:Press Association
The Sun can reveal the Ministry of Defence is looking at plans for a ceremonial funeral.
Chris Curtis, of pollsters Opinium, said: “It demonstrates the positive and uplifting impact Captain Tom has had.”
Heart radio presenter and Britain’s Got Talent judge Amanda Holden launched a petition for a statue outside Parliament.
Writing on the Change.org website, she described Captain Tom as “a national hero who brought us all together and shone so much light in such a dark time”.
She continued: “Let’s show generations to come what it was to be brave, courageous and spirited with a statue of Captain Sir Tom Moore outside the Houses of Parliament forever more.”
Health Secretary Matt Hancock described Captain Tom as an “inspiration” and he promised: “I will ensure we mark his contribution properly and appropriately at the right moment.”
Captain Tom claps for carers in July last yearCredit: captaintommoore/Twitter
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A message at the top of the BT Tower in Central London reads 'RIP Captain Sir Tom Moore'Credit: Alamy Live News
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A screen at Piccadilly Circus, Central London paid tribute to the war veteranCredit: Alamy Live News
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Residents stepped out to pay tribute to Captain Sir Tom in Twerton, near BathCredit: Reuters
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A minute's silence was held in the House of Commons Credit: PA:Press Association
Last night, the PM said he “absolutely” backed calls for a permanent memorial to Captain Tom.
Mr Johnson told a No10 press conference: “We will be working with his family to see what is best to take forward.”
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A group of university students from Brighton join in the national moment of applause Credit: Alamy Live News
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Captain Tom surrounded by his family in Barbados
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A woman in Langport, Somerset leans out of the window to clap for the war veteranCredit: Splash News
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Melvyn Burlace salutes Captain Tom in his front garden in Cardiff, WalesCredit: Getty Images - Getty
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People stand opposite the house of Captain Sir Tom Moore in Marston Moretaine in Bedforshire, to join in with the clapCredit: PA:Press Association
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The hero became a beacon of hope during the first lockdown
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Last July Captain Tom was knighted by the QueenCredit: Getty Images - Getty
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Flags at half mast at Downing Street last nightCredit: PA:Press Association
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Captain Sir Tom poses with his memoir he released in September called 'Tomorrow Will Be A Good Day'Credit: Getty Images
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The Captain at The Royal British Legion's Festival of Remembrance last NovemberCredit: PA:Press Association
The Sun Says
HOW moving last night’s national clap for Captain Tom was.
And how fitting it would be if a major hospital was renamed after him.
Better still, a new one built in his memory.
There are many excellent suggestions for marking the life and legacy of the 100-year-old war hero who raised so much for NHS staff and rallied the nation in the early days of this crisis.
But we have no doubt he would have preferred a new hospital to any number of statues or plaques . . .
No matter how much his admirable feats deserved those accolades too.
A look back at Sir Captain Tom's amazing achievements which captured the nation's hearts