Entitlement to legal aid is a “basic human right”, the Labour leader, Jeremy Corbyn, has told a rally aimed at defending public access to justice.

In a speech at Conway Hall, central London, Corbyn condemned court closures and the withdrawal of legal aid for employment tribunals, welfare benefit cases and other areas of law.

The Labour leader, who used to sit on the justice select committee, said that the number of social welfare cases receiving legal aid support had plummeted from 470,000 in 2010 to only 53,000 cases several years later.

“We will support and defend the principle of legal aid,” Corbyn said. “Courts and law centres are closing down. The opportunity to be represented at employment tribunals has gone. It’s a denial of justice. I would not say that legal aid is an economic benefit, it’s a basic human right.”

Labour has set up a policy review under the former justice minister Lord Bach to look at ways of restoring legal aid. It is due to hold its first session later this month.

Corbyn, who explained that he had had “lots of fun” over the past three days organising a shadow cabinet reshuffle, said he was opposed to US-style justice which produced high re-offending rates.

“I think there’s good in everybody,” he said. “Whatever crime has been committed. You should reach out to support them and [provide] rehabilitation not just punishment.”

Corbyn praised the radical traditions of the venue in Red Lion Square, to which he said he owed his existence: “My parents met in this very hall. They were at a rally protesting about the fascist invasion of Spain.”

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The Justice Alliance meeting was also addressed by the director of Liberty, Shami Chakrabarti, who said cuts to legal aid were “deeply ideological and spiteful”, and the Labour peer Helena Kennedy who said the UK was witnessing “the destruction of one of the iconic” creations of the Attlee post-war government. It also featured a large puppet of the justice secretary, Michael Gove, carrying a list of what he would scrap in 2016.

In a separate development, lawyers representing some of the 90 firms suing the Legal Aid Agency over their failure to obtain a duty criminal solicitors’ contract said disclosure of documents had revealed a basic mathematical error had unfairly robbed one firm, Edward Fail, Bradshaw & Waterson (EFBW), of a legal aid contract.

Jamie Potter, a partner at Bindmans and the solicitor representing EFBW, said: “This scheme has been dogged by controversy since first proposed by the former lord chancellor, Chris Grayling. The error in this case may have been small, but its consequences were extremely serious.”

Paul Harris, a managing partner of EFBW, said: “The LAA has now admitted a basic transcription error that cost my firm a contract. The number of contracts we are awarded significantly affects the extent to which we are able to continue as a business, including as to the number of staff we can employ.

“Can the LAA realistically say that such errors have not been made in respect of other bids by us or by other firms? … livelihoods should not be undermined by the typing of a 1 instead of a 2 and firms should not be required to bring legal challenges to uncover such errors.”

A Ministry of Justice spokesperson said: “We still have one of the most generous legal aid systems in the world, with £1.6bn spent last year alone. The spending review settlement we have reached with the Treasury for the next five years leaves legal aid almost untouched.”

The department declined to comment on the dispute over duty solicitor contracts.