Boris Johnson wants to take on strategic oversight of schools if re-elected as London mayor, claiming only a systemic fight against educational underachievement can tackle the social exclusion that he believes lay behind last summer's riots.

Johnson, who has already launched an inquiry into the state of the capital's education, told the Guardian on Friday that he believed some schools in London were "chillingly bad", adding that it was unacceptable to have 55% of young black men unemployed.

But the mayor went further than before by making a pitch to be given more power over local authorities to tackle illiteracy and innumeracy, arguing that education was the best antidote to the "nihilism" and exclusion revealed by the riots. Several London boroughs already face growing interventionism from central government as part of Michael Gove's education reforms.

Johnson said: "The biggest shock for me from the riots was the sheer sense of nihilism – perhaps I should not have been shocked, but in my view literacy and numeracy are the best places to start. In seven particular boroughs in London one in four children are leaving functionally illiterate. In a few schools it is nearer 50%. We have to intervene at an earlier stage, and I think the mayor can help."

Johnson's aides argue that his battle to reduce joblessness in the capital, and prevent new jobs from going only to highly motivated foreigners, will be hampered if he has no role over standards or in planning the extra 100,000 school places needed in London.

In the interview, he was also unapologetic about the way he campaigned for a cut in the 50p top rate of income tax in this week's budget, even though post-budget polls show the cut is opposed by Londoners by a margin of 55% to 35%.

He said: "I have always argued that London has got to be tax-competitive. I think it is crazy to go on endlessly with a tax rate that is amongst the highest in the G20."

However, he did not defend George Osborne's so-called "granny tax", saying: "I am not the chancellor of the exchequer. I did not write the budget."

He instead repeatedly referred to his decision to make the freedom pass available for 24 hours a day to Londoners from the age of 60, saying: "It is worth several hundred pounds a year and the single biggest reason for older people to be grateful to this administration."

He said: "It may be some aspects of the budget are not going down very well. I am not convinced that I will be necessarily associated with those measures. It is not my blooming budget and it is not necessarily one that I would have written. There is plenty we can do in London to help the poorest and the needy."

Labour will try to pin the blame for the "granny tax" on Johnson, saying he was the leading advocate of the cut in the top rate of tax, and therefore must be responsible for the decision to fund it through freezing pensioner allowances. There are 1.2 million people in London aged over 60, and traditionally they have been inclined to vote Conservative.

Elsewhere in the interview Johnson claimed that:

• The "implosion of [Rupert] Murdoch's power has been the single biggest political event of the past three years", and more significant than the general election.

• The frugality of his first term as London mayor on average saved Londoners £400 in lower council tax bills.

• His superior ability to lobby the cabinet means he is better placed than his Labour rival Ken Livingstone over the next four years to extract vital cash from the Treasury for transport and housing.

• The government has now recognised his case for extra airport runway capacity in the south-east, but "contrary to popular belief I am not the slightest bit wedded to some remote archipelago in the Thames estuary".

Johnson insisted that he was in a tough, tense fight with Livingstone, even though polls this week showed he had stretched his lead to eight points, defying a wider Conservative party poll deficit in the capital.

Johnson's decision to set his strategic sights on education as a key goal for his second term is seen by aides as a logical extension of his existing role on skills, training and employment in the capital. He is said to have been struck by evidence suggesting more than two-thirds of children involved in the August disturbances had special educational needs and a third were excluded from school.

He insists he is not involved in a power grab against the education secretary, Michael Gove, or seeking to reintroduce the Inner London Education Authority, abolished by Margaret Thatcher in the 1980s.

He said of the riots: "There were people who joined in out of a sheer sense of collective intoxification – a kind of madness that gripped a lot of people. But there were people who feel that there is not enough in society for them and were just shockingly nihilistic. We need to know what is going on in these people's lives and why they can feel such a sense of exclusion.

"There are too many people who feel there is no future for them in this city. I want to try to deal with these kids at an earlier age and trying to crack illiteracy – that is at the heart of this. It is crucial that we invest in literacy.

"There are one in four kids reaching the age of 11 who are unable to read properly. That is the best place to start. If you believe the figures, 55% of young black men are unemployed in London. There are some boroughs like Hackney that are very good at tackling this problem in schools, and are really on the case, but there are others that are chillingly bad."

Elsewhere in the interview he defended his progressive record, saying: "I think most right-thinking liberal people will see this as an administration that has been more open, transparent, and progressive than anyone predicted." He promised to find £150m for safer cycling, build a further 55,000 affordable houses and create 200,000 jobs, adding that he would continue to campaign for a living wage.

Johnson also defended his decision in 2010 to dismiss the claims of widespread phone hacking at News International as a load of codswallop and a put-up job by the Labour party. "I said what I did on the basis of the advice I was being given by John Yates [former Met assistant commissioner] about the true state of affairs. No one knew about Milly Dowler's phone being hacked. Nobody knew that kind of thing had gone on. I was informed 'there was nothing new here to be seen, move on, no new evidence' and that is why I said what I said. Clearly that was not a view vindicated by events.

"Given what we now know about media practice, the whole thing has to be pursued to the crack of doom, all collars must be felt, and the stables have got to be cleaned out."

Johnson refused to resile from his broader defence of the role of Rupert Murdoch in liberating newspapers from the print unions' grip. He said: "I don't regard him as quite the satanic influence that some do and if you look at the newspaper industry he did a great deal to set it free, and that is a point you don't often hear these days."

But he said the single biggest change in the British political landscape in the last two to three years "was not really the general election. It was the implosion of Murdoch as a power. That is over and that, I have to say it, is incredible. It is the most spectacular change, and given what is coming out it is patently for the good. If it is true, and it seems to be undeniable, that there was a culture of bribing police officers, bribing health workers and systematic intrusion of people's lives then I think it is great that is all exposed."