It comes as a host of events and funding programmes were announced to mark the 50th anniversary of Churchill’s state funeral, which falls on January 30.
A trio of commemorative events will be held on the day including a special service in the Houses of Parliament, the laying of a wreath in Westminster Abbey and a flotilla along the Thames led by the vessel which carried Churchill’s coffin in 1965.
Speaking after the launch event, Ms Soames, brother of Tory MP Sir Nicholas Soames, was asked whether Mr Johnson shared any characteristics with Churchill.
“Yes. Journalistically, certainly, and wit,” she replied, adding that in the future more leadership similarities may appear.
Asked about Paxman’s suggestion Churchill would be unelectable today, she said: “Well, I just don't think that's true. I think that Churchill's virtues were so great and, in the same way that Boris is very popular, I think Churchill would be very popular because he's got this amazing gift of the gab and he had a genuine commitment to ordinary people.”
Asked if Paxman was wrong, she added: “Yes. Paxman's got a programme to promote. … It's certainly true that Churchill was an egotist and I think Jeremy Paxman may easily be one too.”
Ms Soames also praised the London Mayor’s “absolutely terrific” book on Churchill, saying he had raised his game and produced a “very accessible … warts and all” account.
News that Churchill’s grandchild believes Mr Johnson shares characteristics to the man named the Greatest Briton of all time in a 2002 poll is a timely boost for the London Mayor.
Mr Johnson played down comparisons with the Tory wartime prime minister in the past but was seen by some as courting such suggestions with his recent book, The Churchill Factor: How One Man Made History.
Writing in the Radio Times to mark the 50th anniversary of Churchill’s death, Paxman described him as “a ruthless egotist, a chancer and a charlatan at times”. “Would he be electable now?” Paxman asked. “I fear not. He was a man of his time, a parliamentary one-off who’d be suffocated by the spinning and posturing that pass for politics today.
"Being both good and bad, adequate and inadequate, selfish and public-spirited, is just being human. Maybe — though he or she never seems to have been especially visible — there was someone else who might have led the country in its darkest times.”