Speaking to a Westminster lunch, the mayor repeated his call for the abolition of the 50p income tax rate and urged ministers to do more to boost economic confidence, but brushed off suggestions that he has his sights set on succeeding Mr Cameron as Prime Minister.
Mr Johnson also made a plea for the mayor to be given more powers over education, warning of a "real risk" that the current generation of 18-year-olds will miss out on opportunities in life, in part because of the failure to instil in them the kind of work ethic seen among the foreign youngsters who fill thousands of jobs across London.
As Europe struggles with the ongoing economic crisis in Greece and other eurozone states, the Prime Minister and Chancellor have repeatedly argued for greater co-ordination of fiscal policy within the 17-nation single currency area to boost stability.
Mr Osborne said in August that the "remorseless logic" of the single currency was that "you end up having something akin to a single budget policy", adding that as a non-eurozone member of the EU, Britain should "allow greater fiscal union while protecting our own national interest".
Mr Johnson said today: "I think it would be absolutely crazy to decide the solution to the eurozone crisis is to intensify fiscal union and try to create an economic government of Europe.
"I really can't see for the life of me how that is going to work in the long term.
"Fundamentally, if you look at the ERM (European Exchange Rate Mechanism) experience and what is happening now, you get back to the issue of confidence. If people know the system can dissolve, then obviously they are going to wait for the moment when it does.
"That is the fundamental, inescapable problem that we face in endlessly trying to bail these countries out.
"It seems to me we are slightly living in a fool's paradise at the moment."
Mr Johnson has previously clashed with his party's leadership over the 50p rate of income tax on those earning more than £150,000, and he renewed his demand for its abolition today.
"I don't think we can go on with a top rate of tax that is higher than London's major competitors," he said.
"We have got to look at the competitiveness of London against other capitals and at the moment they have lower tax rates than us. In the long term, I feel that will be a disadvantage."
Despite his support for high-earners, Mr Johnson said some bankers should have faced prosecution and possible jail for their part in the financial crisis of 2007/08.
"I do think it would have been a good thing if they could have found someone to carry the can, absolutely," he said. "I'm afraid I am not sufficiently expert myself, not being a banker, to point the finger, but if you've got someone..."
Abolishing the 50p tax rate should be part of a drive to boost confidence in London and the UK's economic future, said Mr Johnson.
"What the economy needs now, when things are very tough, is not more regulation - and indeed it doesn't need more taxes or a greater aversion to risk," he said. "What we need is confidence. That's what this city and this country needs."
Asked what ministers should do, he replied: "What people need to feel is that there is hope and that the economy is going to turn around. The more the Government can communicate to people that things are coming down the track that are going to transform the country, the better."
His long-cherished dream of an airport in the Thames Estuary could be a "massive generator of employment, growth and hope" which would make London "a go-go city", he said. And he called on businesses to recruit and train young people to ensure that skills are available when the recovery takes off.
The mayor's office is working on a massive scheme to train young unemployed people in London to "retro-fit" homes with insulation, to create jobs and improve energy efficiency.
"People often accuse us of lagging behind on this or that," joked Mr Johnson. "The one thing we won't be lagging on is lagging."
Mr Johnson warned: "Too many of our young people are being consigned to life on the dole and on benefits of all kinds.
"There is a real risk that the current generation of 18 to 24-year-olds will simply miss out and opportunities that we all had won't go their way.
"It would be a fine thing in my view if all us people who care about London and are employers in the city were to take on apprentices, work placements, interns.
"We need to make sure that when the upturn comes - and it will come eventually - we have invested in those people and that human capital."
He said the mayor's office should be given a strategic role in improving education across the capital, to ensure that born-and-bred Londoners have the skills they need to compete with migrants for jobs in the service sector, such as coffee bars.
"There is a problem with young people in London who don't have the educational attainment that they need, particularly in literacy," said Mr Johnson.
"These are early discussions we are having, but if there is something we can do at a strategic level to encourage better outcomes in London, we want to be involved."
He added: "Look at Pret-a-Manger. If you've been to Pret-a-Manger recently, how many native Londoners served you? What's going on? We want to address that problem.
"Somehow or other, it strikes me that young people growing up in this city who are born here are not necessarily getting the encouragement, the skills, the work ethic that they might, or the ability to cope with work, the desire to do the job - whatever it is, there's something missing.
"I don't know what it is. I don't have the answer. They need to be given the skills to compete."
Pressed over whether he had any ambitions to be PM, Mr Johnson accepted that any conversation he might have with journalists on the issue was "meaningless" and "a wonderful charade".
But he added: "The reality is that I was incredibly lucky to get where I got as Mayor of London and it is an immense privilege and a difficult job to do.
"I love it and I want to keep doing it for the next four and a bit years and I'm going to work very hard to do that. As I said to Jeremy Paxman, I really think it will be the last big job I do in politics or in life."
PA
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