Mr Johnson laid out his vision at a dinner in Washington where he was given a prestigious award by the American Enterprise Institute.
The intervention comes as senior Tory MP George Freeman said that Theresa May needs to step down after Brexit in March and make way “for a new generation.”
A recent survey by ConHome of Conservative members has revealed that almost 30 per cent want Mr Johnson as leader, more than double the next most popular.
Since he resigned from the Cabinet over the Chequers deal, there has been fevered speculation that Mr Johnson – who is understood to have the backing of many Eurosceptics on the Tory benches – is preparing to launch a bid to replace Theresa May.
Speaking in a question and answer session for wealthy Americans, Mr Johnson made it clear he wants to bring back the halcyon days of Margaret Thatcher and her domestic agenda which allowed many people to buy their own home and get on.
He said: “Social mobility. If you think back to the great achievements of the Thatcher era, it was about helping people to seize control of their own destiny. It was about buying shares or buying their own homes.
“We need to recover that momentum.
“One of the reasons people voted to Leave was because they felt they were not getting a fair suck of the sauce bottle, as they say.
“People are stuck in entry-level jobs and they’re not progressing. And we’re not focusing on those issues, we’re not helping people enough. People are not being made to feel needed enough. And it’s a serious problem.”
He also made it clear that he feels the future of the world and free trade is dependent on a successful Brexit.
The former London Mayor has been a fierce critic of Theresa May’s controversial Chequers plan which limits the opportunities for free trade deals with the rest of the world and forces the UK to accept EU rules.
He said: “We have a choice. And I would just say to all you scholars and supporters of the AEI — this is a critical moment for anybody who cares about free markets, about competition, about global free trade.
“The UK could be about to come loose of the the European system of regulation and government … able to campaign for pro-competitive policies. That’s the opportunity.
He went on: “There’s a conversation going on about how we achieve it, and it is difficult. But the last thing we want now is for us, the Brits, to be sucked back by the tractor beam of Brussels.
“The EU for all its achievements, it really is no longer right in its current form for the U.K. We’ve done the right thing.
“But having done that, we’ve got to make sense of it. And there is no point at all in us coming out of the EU only to remain effectively run by the EU. If you’re going to take back control, then take back control and use it for a purpose.”
Mr Johnson also set himself up as a unifying figure and said the country needs to come together once Brexit is completed.
He joked: “The best thing possible to unify the country would have been if we’d beaten the French in the World Cup. That was my plan. It’s back to the drawing board We came fourth.”
Mr Johnson’s intervention came as Brexit Secretary Dominc Raab held a telephone talks in the latest round of negotiations with EU chief negotiator Michel Barnier.
After the conversation, Mr Raab struck an optimistic note.
He said: “While there remain some substantive differences we need to resolve, it is clear our teams are closing in on workable solutions to the outstanding issues in the Withdrawal Agreement, and are having productive discussions in the right spirit on the future relationship.
“Looking ahead, we agreed to review the state of play in the negotiations following the informal meeting of heads of state or government of the European Union in Salzburg next Thursday, and we reiterated our willingness to devote the necessary time and energy to bring these negotiations to a successful conclusion.”