Speaking at a party event in Brighton, he pledged to create a social justice commission to help tackle inequality.
Mr Corbyn added it was “not right” that some primary schools in England were having to stage events to raise money.
The education secretary rejected the claim that social mobility was currently focused on the “lucky few”.
The Social Mobility Commission is an independent body that promotes social mobility in England, as well as highlighting the situation across Britain.
Under Labour’s proposals, it would be replaced by a new body with extensive statutory powers and independence.
A minister for social justice would be based in the Treasury and work across all government departments to address inequality.
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Asked how the work of a justice commission would differ from the social mobility commission, Mr Corbyn said: “The approach is social justice for all rather than the ability of a very small number to achieve a higher position in society.”
He added: “The idea of social mobility where you pluck somebody out of poverty and promote them into a private school education or promote them somewhere else doesn’t actually help the majority.”\
Mr Corbyn said “some of the wisest people you meet are actually those that are driving buses, sweeping our streets or working in factories or shops”, adding: “So much talent in our society is absolutely squandered and wasted because of obscene levels of poverty and inequality in Britain.”
Labour has said it wants to create a national education service and increase funding.
Mr Corbyn said: “It’s simply not right that our children should be sent on sponsored walks and sponsored runs and all the rest of it to raise money for basic equipment in schools that should be provided by the public purse in the first place.”
Education Secretary Damian Hinds said Labour’s proposals would “downgrade the importance of social mobility”.
He said: “There is not a conflict between fairness and social mobility – one requires the other… it is about breaking the cycle of disadvantage and making sure that everyone has the opportunity to fulfil their potential.
“Our education system is doing exactly that with the gap between disadvantaged children and those from a privileged background having narrowed at every stage: pre-school, primary, at GCSE and with more disadvantaged young people going to university than ever before.”