Labour leader uses speech in London to call for a high-investment economy and outline more details of his programme

The Brexit vote represented people’s rejection of an economic status quo that had failed them, Jeremy Corbyn said in a speech calling for a high-investment economy with better wages and job security.

Giving the most comprehensive outline yet of his economic programme if he were re-elected as Labour leader next week, Corbyn said the party should “have a good think” about the concept of a universal basic income, an idea mainly proposed so far by the Greens.

“But we need to research and test this policy before we can just adopt it,” Corbyn said, speaking at the London headquarters of the financial news service Bloomberg. “That is why I am looking at the party holding a review to consult widely on this policy.”

Speaking alongside the shadow chancellor, John McDonnell, and the shadow chief secretary to the Treasury, Rebecca Long-Bailey, Corbyn painted the UK’s departure from the EU as a choice between two new economic visions.

Theresa May’s government seemed set on a Sports Direct-type future of insecure and low-paid jobs, he suggested, calling it “a mean-spirited vision that will squander talents and skills”.

He lambasted the government for its lack of vision for a post-Brexit UK, saying that instead the party was “retreating to a 1950s fantasy world” of new grammar schools.

Asked after his speech about his own vision of a future relationship with the EU, Corbyn said he wanted close trade relations. “Hopefully that will be part of a single market,” he said. He also said, however, that any post-Brexit deal should preclude agreements to privatise public services and should not feature current rules on a ban on state aid for industries that not all EU members abided by.

“I’m just making the point that in our relationship with the European market, whatever form it is … we need to make sure we are not signing up to something that actually constrains governments in the future,” he said.

Corbyn also reiterated some of the ideas floated during his battle against Owen Smith for the Labour leadership. He called for a programme of national investment in infrastructure and training, and an emphasis on scientific research and nation-wide high-speed broadband.

He also said the changing global economic situation presented “a deep challenge to the social democratic and socialist tradition of which Labour, new or old, has always been a part”. He added: “It punctures the old belief that it was possible simply to redistribute the proceeds [of] a growing economy to pay for public services. It can no longer credibly be argued, for the majority of people, that free trade and free markets alone will deliver increased prosperity. A future Labour government will have to do more than redistribute income and wealth. It will have to focus on how we earn that income and wealth in the first place.”

Other ideas floated in the speech included giving each new recipient of a national insurance number details on how to join a trade union, and a “Philip Green law” to curb dividends and set rules on adding debt to companies.

This was “an alternative to the drift and decay of the Tories”, Corbyn said, adding: “We can and we will rebuild and transform this economy so that no one and no community is left behind.”

Corbyn is seen as increasingly likely to defeat Smith in the leadership contest. The result is due to be announced on 24 September just before the start of Labour’s annual conference.

On Thursday the bookmaker William Hill said it had received a £60,000 bet on Corbyn to win at odds of 1/16, and had now trimmed the odds to 1/25.