Boris Johnson has launched a bold bid to claim the mantle of Margaret Thatcher by declaring that inequality is essential to fostering "the spirit of envy" and hailed greed as a "valuable spur to economic activity".

In an attempt to shore up his support on the Tory right, as he positions himself as the natural successor to David Cameron, the London mayor called for the "Gordon Gekkos of London" to display their greed to promote economic growth.

Delivering the annual Margaret Thatcher lecture, Johnson also called for the return of a form of grammar schools.

He qualified his unabashed admiration for the "hedge fund kings" by saying they should do more to help poorer people who have suffered a real fall in income in recent years. But he moved to forge his own brand of Conservatism, which contrasts with the early modernising of the prime minister, by claiming that it was "futile" to try to end inequality.

In highly provocative remarks, Johnson mocked the 16% "of our species" with an IQ below 85 as he called for more to be done to help the 2% of the population who have an IQ above 130.

"Whatever you may think of the value of IQ tests it is surely relevant to a conversation about equality that as many as 16% of our species have an IQ below 85 while about 2% …" he said as he departed from the text of his speech to ask whether anyone in his City audience had a low IQ. To muted laughter he asked: "Over 16% anyone? Put up your hands." He then resumed his speech to talk about the 2% who have an IQ above 130.

Johnson then told the Centre for Policy Studies think tank, which helped lay the basis for Thatcherism in the 1970s: "The harder you shake the pack the easier it will be for some cornflakes to get to the top."

Johnson moved to associate himself with what were seen as the excesses of 1980s Thatcherism as he said: "I stress – I don't believe that economic equality is possible; indeed some measure of inequality is essential for the spirit of envy and keeping up with the Joneses that is, like greed, a valuable spur to economic activity."

He made clear, however, that Thatcherism needed to be updated for the 21st century. "I hope there is no return to the spirit of loadsamoney heartlessness – figuratively riffling banknotes under the noses of the homeless – and I hope that this time the Gordon Gekkos of London are conspicuous not just for their greed, valid motivator though greed may be for economic progress, as for what they give and do for the rest of the population, many of whom have experienced real falls in their incomes over the last five years."

Johnson, who is assessing when to return to Westminster to ensure he is in a strong place to challenge for the Conservative leadership when the prime minister stands down, also reached out to the Tory right by:

• Calling for a form of grammar school to be revived as he spoke of the need for academic selection, which he renamed as "academic competition". He also called for the return of the assisted places scheme, abolished by Labour in 1997, in which the state paid private school fees for gifted children from less affluent backgrounds.

• Warning that the accession of Romania to the EU means that London can do nothing to stop the "entire population of Transylvania" from pitching their tents in Marble Arch.

• Calling for his pet project, a new airport in the Thames Estuary, to be named the Margaret Thatcher International Airport.

On the politically sensitive issue of inequality Johnson warned that the growing competition Britain faced in a globalised economy meant that inequality would deepen. He said: "No one can ignore the harshness of that competition, or the inequality that it inevitably accentuates, and I am afraid that violent economic centrifuge is operating on human beings who are already very far from equal in raw ability, if not spiritual worth."

Johnson called for the rich to be hailed for their contribution to paying for public services as he said that the top 1% of earners contribute 30% of income tax. "That is an awful lot of schools and roads and hospitals that are being paid for by the super-rich. So why, I asked innocently, are they so despicable in the eyes of all decent British people? Surely they should be hailed like the Stakhanovites of Stalin's Russia, who half-killed themselves, in the name of the people, by mining record tonnages of coal?"

The mayor added: "It seems to me that though it would be wrong to persecute the rich, and madness to try and stifle wealth creation, and futile to stamp out inequality, we should only tolerate this wealth gap on two conditions. One, that we help those who genuinely cannot compete; and two, that we provide opportunity for those who can."

On Europe, he said it was "time we sorted out the working time directive and time we generally persuaded the Eurocrats to stop trying to tell us what to do".

Johnson said Thatcher would have "comfortably seen off Salmond" by arguing that Scottish independence would have been "the demolition of Britain … lopping the top off the most successful political union in history". But she would also recognise "that England has been so far short-changed by devolution" and give the cities "more powers to raise locally the taxes they spend locally [and] give the politicians an incentive to go for policies that promote growth".

He added: "We may not have many gunboats any more, but we hardly need them, because we are already fulfilling our destiny as the soft power capital of the world – and that is thanks to a woman who knew all about soft power and the deep Freudian terror that every man has for the inner recesses of a handbag."