Boris Johnson, Carrie Symonds, and a baby in a very exclusive club

When Carrie Symonds gave birth to a baby boy, he unknowingly became a member of a very exclusive club.

The newborn son of Boris Johnson, whose name has yet to be made public, is only the third baby born to a serving prime minister in living memory.

In 2000 came Leo, the fourth child of Labour prime minister Tony Blair and his wife, Cherie. Ten years later, there was Florence, born early during a family summer holiday in Cornwall to Conservative PM David and Samantha Cameron.

It is a club that means living the early years in the beating heart of a political machine, with bodyguards by your side and a police officer outside your front door.

For some who experience it, it may come to define you. For others, like Florence, it might just wash over you.

When promoting his memoirs, For The Record, last year, Mr Cameron said Florence, who was only five when the family left Downing Street in 2016, was hazy about his time in power.

He told the Cheltenham Literature Festival his daughter had asked him: "Daddy, is it true, were you actually the prime minister?"

By the time Leo Blair turned one, he had held his birthday party in a swimming pool at Chequers, the prime minister's official country residence; travelled 14,000 miles before he could walk, and was in the eye of a political storm before he could talk.

He made his first "public appearance" when he was just weeks old.

But soon after he was at the centre of a row over privacy, when "unauthorised" photographs of him were used by newspapers in spite of pleas by the Blairs.

At the time, Tony Blair described how having a baby in Downing Street kept him in the "real world".

"I can be about to leave Downing Street for Prime Minister's Question Time, my head can be full of 50 questions that the Opposition might ask me that I have no easy answer to, and I nip back up to see Leo," he told the Sunday People.

"And it all comes into perspective. He's playing with his toys and you have to enjoy and savour that and it's a good reality check, isn't it?"

Cherie Blair, mother of Leo who is now 19, said she was sure Ms Symonds, 32, would get "the best care".

In an interview on ITV's Lorraine before the birth was announced, Ms Blair said: "I think for everyone being pregnant at this time, with the constraints there will be on how people can support you, it's a difficult issue but I am sure she will absolutely get the best care."

But she warned "doing it in the public eye" would be an additional strain.

Linda Blair, a clinical psychologist, said staying serene would be the best way for first-time mum Carrie Symonds and Boris Johnson to tackle any criticism in the British press.

"It's not so much how they handle it, it's how they react to it," she said.

And the good news for little baby Johnson?

"He will thrive," says Linda Blair, no matter what the environment in Downing Street.

"That child will accept the situation - what other world do they know?"

In fact, she says, he's the ideal age.

"I don't know how long Boris Johnson will be in office but he will probably be out by the time it would matter, when they are wanting to mix with peers so that won't be a problem. It can be more difficult for teenagers," she says.

And of the inevitable high stress levels circulating in Downing Street, she says: "Until children are four or five their stress levels are determined by the parents' mood so the stress levels in Downing Street won't mean anything to the child, it'll be how the parents react to them."

The last babies born to prime ministers before Leo, Florence and now baby Johnson arrived more than 150 years ago.

Before Mr Blair, Lord John Russell and wife Lady Russell produced the last child to be born to the office holder of First Lord of the Treasury - the prime minister's official title.

Lady Russell gave birth to two sons, George and Francis, during her husband's first stint in office between 1846 and 1852.