Two-thirds of Britons still believe who you know matters more than what you know when it comes to getting on in life, a survey has found.
The poll also found that three-quarters of the population believe family background has a significant impact on a person's life changes.
The survey, for the Social Mobility and Child Poverty Commission, found 84% of people believed employers should pay wages that better reflect the cost of living to support the working poor.
Schools such as Eton are renowned for providing social connections
The poll of 2,272 adults found 65% of the public thought "who you know matters more than what you know" in Britain today.
Some 76% believed family background significantly influences an individual's chances of doing well in life.
But there was a split when people were asked about their own background, with 41% agreeing and 41% disagreeing that their parents' income had influenced where they had got to in life.
Seven in 10 people (72%) thought a good education was the key to getting a good job but nearly half (49%) thought it remained out of reach for most children from lower income families.
Two-thirds (66%) thought government had a role in tackling in-work poverty and 75% thought the government should top-up the incomes of the working poor.
Some 84% said that employers should be providing more opportunities for progression for their employees.
The Commission's chairman, former Labour minister Alan Milburn, said: "These findings show the high levels of public concern about unfairness in Britain.
"Flatlining social mobility and rising child poverty is not a viable proposition for our country.
"Both government and employers should heed the call to pay decent wages to help the forgotten five million people who are the working poor."
Anne Marie Carrie, chief executive of children's charity Barnardo's, said: "The public's overwhelming belief that it's income, education and jobs that drive life chances must now guide the Government to take urgent action to improve children's futures.
"Poorer children are scarred by a development gap that widens from the cradle onwards, limiting their vocabulary by the time they start school and increasing the likelihood they'll be unemployed when they leave.
"The Government must intervene throughout children's lives to ensure the poorest children can thrive. "
A Government spokesman said: "Our welfare and education reforms will help families to find and progress in work, support aspiration and ensure that children growing up today are equipped to get good jobs in the future."
The spokesman added: "Work remains the best way out of poverty, which is why we are reforming welfare to make work pay.
Our welfare reforms will improve the lives of some of the poorest families in our communities, making three million people better off and lifting up to 250,000 out of poverty.
"We are committed to the minimum wage and encourage employers to pay above the national minimum wage when they are profitable and when it's not at the expense of jobs."