. "I think it's sad, incredibly sad, and they miss out."
Ms O'Grady, who has led the TUC since 2013, insisted that state schools offered "real benefits" such as teaching children empathy. "You have to mix with people from all walks of life," she said.
State-school pupils could "understand that not everybody lives the same life as you, whatever life that is", whereas those whose parents had chosen for them to "only mix with people like them" were not afforded this privilege, she added.
Ms O'Grady said she was aware of the danger of sounding like she was "having a go at the posh" but that this was not her intention. "This isn't being tongue-in-cheek," she said. "I actually believe there are real benefits to the state system that you simply would not get in the private sector."
Ms O'Grady, who was educated at Milham Ford School, a grammar that became a comprehensive while she was a pupil there, said she believed the shortage of state-educated politicians had a damaging effect on policy.
"I think people are getting pretty fed up - when they look around the Cabinet table, how many of them had the benefit of a state education? Not too many, and yet they appoint themselves as experts on it."
She said that among the general public, there was a "sense that there's an elite that is setting out the direction for our education system".
"They haven't listened to parents or teachers, and are like bulldozers pushing through a particular path that most people feel worried about," she said.
Ms O'Grady added that her concerns about the dominance of the privately educated in politics also extended to the media, finance and law.
"It seems to me that [the prominence of the privately educated] is fundamentally unhealthy and it's precisely the kind of demonstration of the power of an elite that people feel generally unhappy with at the moment," she said. "They think they're out of touch, don't understand most people's lives and don't necessarily have ordinary people's best interests at heart."
Ms O'Grady's comments came as independent schools launched a new drive to dispel the perception that they were "bastions of privilege".
TES reported last month that fee-paying schools were set to publish details of their partnerships with state schools on a new website ("We're not elitists in ivory towers, say private schools", 20 March). The move is designed in part to counter what one headteacher described as "sweeping, simplistic generalisations" about fee-paying schools.
Barnaby Lenon, chairman of the Independent Schools Council (ISC), said that Ms O'Grady was "out of touch with the realities of life in many independent schools".
"She may be surprised to learn that our schools are very diverse and don't all fit the stereotype she is describing," he said. "In reality, many are local or smaller schools, well known in their communities, with more than 28 per cent of children from ethnic minority backgrounds. Many hard-working families from all walks of life will choose to pay, even if it is a struggle, to send their children to our schools."
Mr Lenon said that ISC schools helped more than 40,000 children with their fees and that more than 5,000 pupils paid no fees at all. "Our schools are keen to continue widening access to children, whatever their background," he added. "That is why our schools gave more than pound;660 million in fee assistance last year and will give even more this year."
`Our unions have been amazing'
Frances O'Grady, pictured right, says she is not sure what teaching unions could have done differently over the past five years to win a better deal from the government.
Members of the largest teaching unions, the NUT and NASUWT, have taken strike action over pay and pension reforms but have won few concessions.
"Our unions have been amazing when you think what they've faced," she says. "Throughout this government, they've had Michael Gove, who didn't always take an evidence-based approach to education. They've had 15 per cent real-terms pay cuts, they're having to work longer for less.
"I think teachers have responded with enormous forbearance in a very difficult situation."
Ms O'Grady says that unions have "genuinely" tried to negotiate but have not been treated with "the respect they deserve".