Failure by Britain's comprehensive schools risks fuelling the drift by jobless and unskilled groups toward extremist organisations such as the English Defence League, the government's chief inspector of schools, Sir Michael Wilshaw, has warned.

The consequences of underachievement in state schools are a grave moral and political danger, as well as an economic failure, Wilshaw said in an interview shortly after he opened a national debate with research suggesting that many of England's most talented children were failing to reach their potential.

For many of the most able, that failure locks them out of Britain's most prestigious universities. But for others the consequences of underachievement could trap them in a lifetime of poverty.

"We've got to worry about those parts of the country where youngsters aren't achieving as well as they should, and therefore can't get jobs in the knowledge-based economy. And where those youngsters aren't getting jobs, then they will be attracted to organisations like the EDL, and we need to worry about that as a society," Wilshaw said.

"Underachievement – especially now that unskilled jobs are diminishing by the day – in school, in education, has serious consequences for society because these youngsters won't be able to get jobs. There aren't the unskilled jobs out there in the way that there were when I started teaching. I was teaching the sons and daughters of dockers. The docks have gone, the shipbuilding yards have gone. The mines have gone.

"Youngsters now need more skills, more qualifications, more training than ever before."

While this week's research by Ofsted focused on the children who were top performers leaving primary school, finding that two-thirds were unable to go on and achieve similar results in GCSE examinations, it also highlighted inequalities among sub-groups that did significantly less well, especially those eligible for free school meals, boys and white British students.

But on the educational problems involving white boys in particular, Wilshaw cautioned: "It may be the problem now but a few years ago it was Afro-Caribbean youngsters, but actually that's not such a problem now. Things change very quickly. We might say it's white boys now, but we might not being saying that in 10 years time, so we've got to be careful about this and not stereotype particular groups of youngsters. There are schools up and down the country that do well by white boys."

Wilshaw is preparing to kickstart his second national debate of the month, when he gives a speech on Thursday which he said would discuss "what we need to do as a nation to address the needs of our poorest children, most of whom reside in white British populations. It is an issue that can only be tackled by central government, taking very clear and decisive action on this.

"I won't stop worrying about it, and nor should the nation, until we get more bright youngsters from ordinary backgrounds who've gone to comprehensive schools into leading positions in society. We should all worry about that," he said.

"We want the leading politicians coming from comprehensive schools, the judges coming from comprehensive schools, the lawyers, solicitors and surgeons, all coming from comprehensive schools. That would be good, wouldn't it? Rather than coming from the selective system or the independent sector. It's important that we focus on it."

The truth, Wilshaw said, was that non-selective state schools had a more demanding role than their counterparts in the independent sector, which he appeared to suggest were soft in comparison.

"Comprehensive schools have a more difficult job. They are teaching the most able children as well as the least able. They are teaching children from a diverse range of backgrounds. They are teaching youngsters who could come from difficult backgrounds. They have more behavioural issues in the state sector.

"And yet we want our most able children to do really well, and I would look to the independent sector to help and support the state system in a variety of ways."

Wilshaw said independent schools should be doing more to help.

"My view is that they are part of a whole system that needs to do well. I'm sure they want this country to be a cohesive society. I'm sure they don't want such big gaps in performance between the poorest children and the most prosperous children to be so apparent.

"It's up to them to try and narrow those gaps, along with teachers in the maintained system."

As a successful headteacher at Mossborne Academy in Hackney, north London, Wilshaw said he tracked his most able students as carefully as the less able.

At his press conference to introduce the research, Wilshaw referred to "parents who can't provide a supportive home environment" as one factor holding the most able back. "Most parents that I've met love their children but some find it very difficult to support their children in terms of educational provision and support at home, for a variety of reasons, economic reasons, difficulties at home, whatever," he said.

"I think then it's the responsibility of schools to intervene very quickly and ensure they become surrogate parents for those children. I've said that ever since I became a headteacher."

He conceded that put pressure on teachers. "But there's huge enjoyment as well. We shouldn't see the negative side of it. A lot of my teachers at Mossborne and St Bonaventure's, where I was head in the 80s and 90s, worked with the children late into the evenings, enjoyed coming in on Saturday mornings. They want to see those children doing well. There's great pleasure from it."