Days after a shocked Tony Blair, aged 46, and his wife, Cherie, 45, announced that they were to be the parents of the first child born in wedlock to a serving prime minister in more than 150 years, this reporter found himself in the prime minister’s office asking him about his choice of contraceptive.

It is probably the first and last time the issue had come up in an interview with a serving prime minister. But my strong memory is that my editor at the time had absolutely no interest in the 2000 London mayoral elections, the ostensible subject of the interview, and only in how Blair, three years into his first term and racked by Northern Ireland, had inadvertently become a father for the fourth time, and what it would mean for his prime ministership.

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The impact of the patter of tiny feet on the inner workings of No 10 and the decisionmaking of a stressed prime minister has since become a matter of growing curiosity as Britain’s prime ministers, or their wives, have become younger.

The Blairs’ surprise fourth child, Leo, delivered by the royal surgeon, Marcus Setchell, managed to survive seven years in No 10 despite a querulous neighbour lobbying for his father to leave the house, and by all accounts is now a well-adjusted boy. He attended his father’s speech last week on 120 years of the Labour party and is, in his dad’s judgment, already an excellent political strategist.

Facebook Twitter Pinterest Tony Blair with Leo on the steps of No 10 with, left to right, Nicholas, Kathryn, Cherie and Euan. Photograph: David Sillitoe/The Guardian

So whatever progeny emerges from the union between Boris Johnson and his fiancée, Leo is proof that children need not be scarred by being raised in a minor stately home in central London in which abnormality is the rule, and privacy largely dependent on the judgment of newspaper editors.

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Leo was an exception only in that he, and subsequently Florence, the youngest child of David and Samantha Cameron, were born to serving prime ministers. Many besides Johnson, Blair and Cameron have been prime ministers with relatively young children. Even those who came into No 10 with children in their 20s such as Harold Macmillan liked to fill the house with children’s parties, just to lighten the sombre mood the place can exude, especially at weekends.

Not that these celebrations with the progeny of politicians always go smoothly. In her new memoir, Kate Fall, David Cameron’s deputy chief of staff, recalls a weekend at Chequers where one of Michael Gove’s children marched into the room followed by a flustered Cameron child saying: “It’s true, isn’t it, this will be our house when Daddy become prime minister?”

Facebook Twitter Pinterest David Cameron leaving No 10 for the last time as prime minister with Samantha and their children on 13 July 2016. Photograph: Sean Dempsey/EPA

Sajid Javid’s 10-year-old daughter, Maya, has also left some pointed advice hidden in a book in Dorneywood, the government grace and favour mansion in Buckinghamshire, on how prime ministers should treat their chancellors.

However, some children such as Carol Thatcher did suffer but whether that was the mother or the home can be disputed. Lord Butler, once Margaret Thatcher’s principal private secretary, recently recalled vividly “going up to the flat and into the sitting room to discuss some point with Margaret Thatcher and in the course of our discussions I heard a rustling in a cupboard in the corner of the room.

“And I said: ‘What is that? Are there mice up here?’ And she said: ‘No, that’s Carol.’ I said, ‘Why is Carol in that cupboard?’ And she said, ‘Well, you know, she was wearing jeans so I told her to hide herself while you were coming in.’”

Thatcher’s whole approach to motherhood was flawed, according to her admirer Lord Powell, who served as her foreign policy adviser and private secretary. He recently recalled: “The challenges of being a mother and prime minister were considerable and, to be perfectly frank, she rather failed. She didn’t have time enough for her children. She rather overindulged Mark when she perhaps underindulged Carol.”

Some prime ministers never tried to blend No 10 as an office and a family home. Mary Wilson, for instance, installed a doorbell in her second-floor rooms to make sure no civil servant intruded. The only informality came from a dog called Paddy and a cat named Nemo. Norma Major took it to a further extreme and lived separately with the young children in Huntingdon for some of the time that John Major was prime minister.

The twin risks that prime ministers with young families say they face are balancing work and life, and ensuring a form of privacy or normality. Cameron and Blair had a legendary ability to compartmentalise, probably born of intellectual self-confidence, so when they left the study and went upstairs, the work mentally stayed downstairs. In the case of Cameron, this transition was helped by a short whisky and Game of Thrones episode.

Cameron also prided himself on his normality, which his wife, Samantha, attributed to their both having large families.

“We have a lot of focus on being on our own, keeping up with old friends, we’ve got big families. I am one of eight siblings, he’s one of four and I think that keeps you grounded. You’ve got to try and not let your life change in any way,” she said. Guests in the Cameron Downing Street living room were expected to balance kids on their knees.

For Gordon Brown, normality, and family time, came temperamentally harder. A natural workaholic and worrier, his family holidays were cut short by the foot and mouth crisis or a seminar on the financial crash. Sarah Brown tried hard to compensate, once writing: “I believe that part of my role as wife of the prime minister is to make an often extraordinary life as ordinary as possible for myself, my husband and my children.”

In the case of Boris Johnson he has been around the fatherhood course almost innumerable times but the idea that any aspect of his life will be normal, even doting fatherhood, is implausible.