Mr Stewart tells of his "special connection" to the Jewish community only days, after quitting Boris Johnson's Conservative Party to stand as an independent candidate for London Mayor.
The former International Development Secretary reveals details of his own family background he says he is determined to "re-explore" as he campaigns to topple Sadiq Khan in next year's poll.
Mr Stewart, who was educated at Eton and Balliol College, Oxford says that his mother's father was "a Jewish doctor in Wimbledon" while his American wife Shoshanah's mother was also of the faith.
"We celebrate Jewish festivals, but also Christian festivals too," he says of family life, with his two children aged four and two.
"We are a little bit eclectic - so my boys celebrate Chanukah and Christmas as well."
Mr Stewart says: "One of the lovely things about today is about exploring my own heritage... I feel a very, very strong link."
Looking ahead to his campaign up until the May 2020 election - at which he also stand against the current mayor and Tory hopeful Shaun Bailey - he adds: "For me, a lot of the next few months is just about listening, walking and learning...
"In Golders Green just now I was pushing people to take me down side streets, take me into shops, show me synagogues.
"I want to hear people talk about their own lives and their families to develop as rich a picture as I can of life and variety.
"One of the things that is obviously true is that the Jewish community has many divisions and differences within it.
"I can't assume just because my mother comes from a Jewish family that her experience is the same as everybody elses."
Mr Stewart had earlier spent Monday morning visiting Golders Green, chatting to locals and also visiting the Headroom Cafe, where he spoke with Jami Chief Executive Laurie Rackind and Chair Adam Dawson about mental health issues facing the Jewish community.
The tour, which had been arranged by the Jewish Leadership Council before Mr Stewart decided to quit the Tories and announce he was standing for London Mayor, also saw him meet with Union of Jewish Students representatives at JW3.
Speaking to the JC afterwards, Mr Stewart, who was elected as the MP for Penrith and The Border in May 2010, says his great-grandfather and great-grandmother were both Jews from "what is now Romania" in the 1870s.
"Technically he was from what would have been part of the Ottoman Empire and she would have been in what would have been Austria- Hungary," he explains.
"We still have in our house Hebrew texts that they would have brought over with them.
"They had moved to New York and then moved to London in 1900. From a photograph my great-grandfather has the look of a very traditional Ashkenazi man of the time."
Having been born in Hong Kong, and having lived in the "not very Jewish area" of South Kensington, Mr Stewart says he will relish the opportunity of delving further into his Jewish past that the forthcoming months of mayoral campaigning would allow.
"This community has a special connection to me because of my own family," he adds.
"But I'd like to try to do the same with almost every community. It is so important is to also approach this job with a certain amount of humility.
"I mean this is a city of nearly nine million people, more communities than you can believe. It's been one of the biggest management challenges in the world for 200 years."
Mr Stewart is quick to reject suggestions that, by standing against the current Labour Mayor Mr Khan, he is seeking to split the centrist, progressive vote in the capital.
"What you want to do is choose a good mayor," he says. "The lovely thing about democracy is that you really do get to choose, one person, one vote, on who you think is going to make this city better in five or ten years' time.
"Who is going to really address crime, build houses rather than talk about building houses.
"I'm very confident the mayor himself would not want to feel as though he was getting special treatment - either because of his political party associations or because of his ethnicity.
"He'd want to be judged on his performance."
Mr Stewart said it must be recognised that while religious and ethnic background are "one aspect" of a person's life - issues such as mental health, poverty and wealth and air pollution are universal issues.
He also explains his decision to leave the Conservatives - and his open differences and criticism of the path now chosen for the party by Mr Johnson.
A Remain supporter in the 2016 referendum, he went on to back then Prime Minister Theresa May's withdrawal deal.
Responding to the suggestion that Mr Johnson is very different as prime minister to the socially liberal version who was London Mayor until 2016, Mr Stewart is quick to agree.
"What's changed?" he opines. "It's difficult to know what is going on in his head. I really don't understand that and I wouldn't presume to judge it.
"But you are right - he has clearly, as far as I'm concerned, decided to crank the Conservative Party round to the right.
"He' s going after these votes. His strategy seems to be to pick up votes in the north east of England from traditional Labour voters who might have voted Labour but are actually very right wing in their social attitudes.
"I think once you've done that it's difficult to come back. He keeps suggesting, 'Oh it will be fine, once I've got Brexit done I'll come back to the centre ground again.'
"I don't think you can. Once you've picked up 60 constituencies of that sort you are taken hostage by it."
Mr Stewart says he has "profound differences" with not just the Conservatives under its new leader but also the "way Jeremy Corbyn would take things".
"Populism has a terrible, vicious momentum of its own," he adds.
"This is a society in Britain that was until quite recently was really quite a miracle - a much more consensual society than the United States for example.
"There are you know Democrats and Republicans are quite hostile tribes."
Having "worked overseas" in Indonesia and in the Balkans, Mr Stewart says he has witnessed politicians "in a matter of months drive people apart."
He served in the UK Diplomatic Service and as a former deputy-governor of two Iraqi provinces, having also walked for 21 months across Iran, Afghanistan, Pakistan, India and Nepal, which led to a bestselling book.
He added: "I don't like politics that divides. I think the whole idea of division in politics is dangerous.
"If you pit the people against parliament, rich against poor, Remain against Brexit, rather than treating people as fellow citizens engaged in a joint project you are doing something dangerous.
"One of the main reasons I want to be an independent and speak as an independent is to not have any of that baggage.
"In the end I'm just running to represent London as best as I can."
