Last month clever-clogs Jo, 41, who can be pleasingly monikered Jo-Jo, hogged the spotlight when he was appointed head of David Cameron’s policy unit. A left-field choice, given that he’s a Europhile, but presumably the PM is abiding by the principle that it’s wise to have one Johnson already in place pee-ing out of the tent before the other squares up to pee into it.

And, now, hauled out of obscurity, we have burly, charismatic Leo: Lo-Jo, 45, complete with trade-marked Johnson thatch, air of well-bred amiability, deep voice, impeccable manners and charming self-deprecation.

He’s non-political, undecided about where he stands on Europe and his main claim to fame thus far is shooting his big brother in the solar plexus with an air gun, a brush with fratricide that could have stymied Boris’s political career before he’d even made his panel-show debut.

“I wasn’t aiming to kill him,” beams Johnson, who was eight at the time. “It was more a display of skill. I wanted to demonstrate that I was able to miss him by just the smallest margin, so he would feel the cool air of the bullet whistle past him. But I, um, got the angle wrong.”

Boris, who was hit in the stomach, apparently leapt up in slow motion “like a Nasa take-off” and had to be taken to hospital, although Leo appears to have forgotten that particular detail, learn more about this.

“Look, I acted on impulse, it was the right thing at that moment and I stand by that,” he says, in eminently reasonable tones. “But it did take place when we were living in Brussels, so maybe it coloured Boris’s view of Europe…?”

More to the point, did the botched assassination colour his view of his brother? To his credit, it did not.

“Boris was fine – I’d shown mettle, and frankly, the occasional mishap was the just the cost of doing business.”

The cost of being born into the Johnson business was indeed substantial. The children’s upbringing was a curious mix of privilege and neglect, common among the upper classes. As a newborn, Boris was left in the back of a car while his parents went off to lunch; when they were small children, any one of the brood might fall off the back of a moving vehicle or be overlooked and lost.

But it certainly toughened them up. As did their father, politician and author Stanley, who left the day-to-day child rearing to his first wife, Charlotte, and concentrated on instilling a fiercely competitive spirit into their four children. He described Boris as “the great prodigious tree in the rainforest, in the shade of which the smaller trees must either perish or struggle to find their own place in the sun”. Sibling rivalry is tough at any time, but how much more so when the eldest is presented at the outset as primus inter pares?

“My family have a manic urge to do things,” observes Johnson. “We were always busy. I was the middle child and so always fighting for oxygen. I’m very close to all my family but I’ve fallen out with all of them at some point – too many elbows.”

The boys attended Eton, while Rachel was sent to St Paul’s. All went on to Oxford. When Johnson père remarried, he fathered two more children, Max (who moves and shakes in Asian finance) and Julia (a talented musician), both of whom followed the same academic trajectory.

Johnson doesn’t remember much about David Cameron, who was two years above him at Eton, other than that he “seemed like a really nice guy”.

One key difference between Johnson minor and his older brother was apparent early on. “I wasn’t a member of the Bullingdon Club. Never. Not ever. Not in a million years. Not ever, never,” he repeats. Was that because he thought they were a bunch of toffs and tossers?

“The Bullingdon Club just wasn’t where the fun was,” he insists, declining to be drawn. “I was much more interested in having a series of dysfunctional relationships with various girls.” Equally crucially, Johnson wasn’t – and still isn’t – a Tory. “I agree with the Tory policy of having faith in people to manage their own affairs and do amazing, inspiring stuff. But I also believe that great entrepreneurial start-ups really need help from central government,” he says.

“China is investing $1.3 trillion in seven strategic sub-sectors, including clean energy technology and new energy cars and biotechnology. But in this country, innovative businesses can’t get finance!” he cries. “Banks are risk-averse because they have to look after little old ladies’ pensions, and venture capitalists want to see a proven track record before they will get involved, so there’s a ‘valley of death’ where exciting businesses are languishing for want of backing.”

Johnson’s environmental activism is firmly, shrewdly rooted in economics and the creation of “producer-led growth” rather than in a consumer-led economy fuelled by cheap credit.

“I want to see innovative products that fulfil a real need, like solar batteries that can heat and power homes in the developing world that previously relied on kerosene, rather than the marketing of another pair of Nikes with inbuilt Twitter feeds.”

His partnership at PwC came about after the firm bought up Johnson’s Sustainable Finance Ltd consultancy. He is also a Visiting Fellow at the Smith School of Enterprise at Oxford, and has presented BBC World documentaries, including One Square Mile and Develop or Die, and written a number of books.

Later this year sees the publication of The Turnaround, an examination of sustainability and the state of the planet. Given the lackadaisical rate of decarbonisation, things are not looking great on the global front, but Johnson refuses to lose hope.

“I am the spirit of optimism incarnate. I’m an addict, a junkie for the stuff that helps me see the light at the end of the tunnel,” he says.

Home, for Johnson, is the unsung London borough of Brent, where he lives with his Afghan wife Taies Nezam – “my big love” – who is a social development specialist in the field of post-conflict resolution. They met on August 31, 1993 in Washington, when he was on stage with a band singing Clash and Rolling Stones covers, badly.

“We were the World Bank Interns, literally, and the most spectacularly uncool group on the planet,” he says, chuckling. “Tries was the only person in the hall paying any attention, and afterwards she came up to me with a straight face and said: ‘Can I be the president of your fan club for the Tri-state area?’ In that moment, I fell in love with her.”

The couple have two daughters: Lula, aged nine, and six-year-old Ruby Noor.

“They attend a posh-ish school but I really don’t want their minds to be narrowed, so at some point we will probably move to the US, because my wife has dual citizenship.”

She also, notoriously, insists on the occasional JFW, or Johnson-Free Weekend. But given that it was Leo who steered Boris towards his bike initiative, we might have to slap an export ban on him. “I can’t take full credit for Boris bikes, but I did encourage him to adopt what was Ken Livingstone’s policy originally. Ken is a great man.”

I can’t help wondering how alleviating world poverty one solar-powered battery at a time can possibly square with having a brother who makes headlines by agreeing to a ping-pong match against Pippa Middleton.

“It’s just not squarable,” shrugs Johnson. “I love Boris intensely and he’s got a tremendous platform where he can do extraordinary stuff that affects people’s lives, but there’s a media circus that goes along with that.”

Comparisons, then, are invidious – or most of them, at any rate.

“But you know, I am just a bit taller,” interjects Johnson with a huge grin. “And I could whip his ass any time at ping pong.”

2 Widgets. We may be putting UK firms at a long-term disadvantage if we are no longer able to influence the setting of standards and regulations in Brussels. There may be a risk, if we leave, that our partners would be so piqued and irrational as to try to stitch things up against us.

3 Global influence. The EU is arguably better placed to strike trade deals with the US, or China, than the UK on its own, though this proposition is plainly untested, and the idea of an EU “Common Foreign Policy” is plainly a joke. Where was the EU on Iraq, or Libya? What, come to that, is the EU position on the Falklands?

4 Perception of UK. It is often said that our strategic significance for the Americans or the Chinese depends on our membership of the EU; though, again, this is untested. More generally, there is a risk that leaving the EU will be globally interpreted as a narrow, xenophobic, backward-looking thing to do.

There may be other good reasons for staying in, but I can’t think of them now. On the other side of the ledger let us consider the advantages of getting out.

1 We save money. We would no longer have to cough up for the EU budget, and could spend those billions in the UK.

2 We get back our sovereignty – especially over our borders, where we would no longer be in the mad position of being forced to extend our entire welfare system to anyone from Bulgaria or Romania, while keeping out lucrative Chinese tourists to achieve immigration caps.

3 We make our own laws again. We would no longer be forced to accept the vast corpus of EU regulation and legislation – much of it too detailed and interfering – that has added to the costs of British business; though we would also find ourselves being forced to comply, thanks to the sheer lunar pull of the EU market, if we want to continue to export to Europe.

4 We can no longer blame Brussels. This is perhaps the most important point of all. If we left the EU, we would end this sterile debate, and we would have to recognise that most of our problems are not caused by “Bwussels”, but by chronic British short-termism, inadequate management, sloth, low skills, a culture of easy gratification and under-investment in both human and physical capital and infrastructure.

Why are we still, person for person, so much less productive than the Germans? That is now a question more than a century old, and the answer has nothing to do with the EU. In or out of the EU, we must have a clear vision of how we are going to be competitive in a global economy. In the meantime, we need a much more informed debate about the pluses and minuses of EU membership, and my economic adviser Gerard Lyons will be leading an attempt to blow away the froth and give people the facts.

This renegotiation can only work if we understand clearly what we want to achieve: a pared-down relationship based on free trade and cooperation. And our partners will only take us seriously if they think we will invoke Article 50, and pull out, if we fail to get what we want. If we are going to have any chance of success in the negotiations, we need to show that the UK is willing to walk away.

However, he added: “It follows from our desire to have a renegotiation that we must also be prepared to say, OK, fair enough, we can’t get the terms that are suitable, then we will walk away.”

He said the debate about the future of the EU was happening all across Europe, not just in the UK because of the “stratospheric unemployment rates”, arguing that the single currency was driving change to democracies.

Europe is “not competitive enough, open enough or flexible enough”, Mr Cameron said, adding Europe “must be flexible enough to accommodate” countries that are members of the single currency and those that are not.

He vowed to “stand up and defend” the UK’s financial services industry, particularly against damaging legislation from Brussels. The City is a “massive advantage” to the UK, he said, and warned that “we shouldn’t spend our time in politics bashing banks.”

He said that European leaders shouldn’t be “surprised” that the UK has opposed efforts to cap bonuses and introduce a financial transaction tax since London hosts 40pc of the EU’s financial services sector.

The Prime Minister said Britain faced a “sink or swim moment” in a global economic race and must drive economic reforms, including a new relationship with Europe, to stay on top.

He said the Government is driving through tax reductions, welfare reforms, infrastructure investment and trade deals to ensure the UK stays competitive globally.