Their fundraising efforts form part of the Captain Tom 100 in which people are encouraged to create their own charity challenge around the number 100 in a bid to continue with his remarkable philanthropic efforts.
Elsewhere, Dame Judi Dench has agreed to eat 100 chocolates, while Joe Root will hit a cricket ball 100 times.
The event is due to begin on Friday – which would have been the Second World War veteran’s 101st birthday – and runs until 3 May.
Sir Tom raised more than £32 million for the NHS after walking 100 laps of his garden using his mobility frame before his 100th birthday on 30 April 2020.
He died at Bedford hospital on 2 February after testing positive for Covid-19.
His daughter Hannah Ingram-Moore said: “The whole Captain Tom 100 challenge was something that my father was firmly round the table talking with us about.
“It has his imprint in it,” she said.
“There was only one thing we could do and that was carry on what my father started by walking 100 laps of the runway, the driveway that became so famous.”
The family intend to walk 100 laps of their garden in Marston Moretaine in Bedfordshire over the course of the weekend.
Ms Ingram-Moore said that walking the laps together would be a “reflective” time for the family.
“It's tinged with a little sadness but mostly absolutely about hope for the future and ensuring that his lasting legacy of hope lives on,” she said.
Sir Tom would have been “so impressed by some of the incredible challenges people are coming up with”, she added.
His 12-year-old granddaughter, Georgia, said the challenge was about making sure you “do what you love, like baking and sport, anything you love”.
And his 17-year-old grandson, Benjie, described Sir Tom’s achievements during the pandemic as “amazing”.
He said: “I know he would be smiling as well and that's the most important thing.”
Organisers of the fundraising event are encouraging people to join in by using the hashtag #CaptainTom100 on social media.
In July last year, Sir Tom was knighted by the Queen in her first official in-person engagement since the start of lockdown for his fundraising achievements.
Sir Tom described the event as “an absolutely outstanding day”.
He said: “I am absolutely overawed.
“This is such a high award and to get it from Her Majesty as well - what more can anyone wish for? This has been an absolutely magnificent day for me.”
Following his death, Prime Minister Boris Johnson described Sir Tom as “a hero in the truest sense of the word”.
He said: “In the dark days of the Second World War he fought for freedom and, in the face of this country’s deepest post-war crisis, he united us all, he cheered us all up and he embodied the triumph of the human spirit.
“He became not just a national inspiration, but a beacon of hope for the world.”