Sheffield has moved closer to becoming one of the first UK cities to trial universal basic income after the council formally lent its support to the idea.

Last month, the shadow chancellor, John McDonnell, confirmed a Labour government would pilot UBI if it won a general election, identifying Liverpool and Sheffield as potential areas for pilot schemes.

The plan would do away with the need for welfare as every citizen would be given a fixed sum to cover the basics, whether they are rich or poor, in work or unemployed.

On Wednesday, senior city councillors agreed to work to ensure a UBI “can be implemented successfully in Sheffield”.

The politicians were persuaded by a detailed proposal put forward by UBI Lab Sheffield, a grassroots group of researchers and activists. They estimate a pilot involving 4,000 people would cost between £18m and £60m, depending on the extent of the scheme.

Julie Dore, the leader of the Labour-controlled council, said she recognised the transformative effect UBI could have on the residents of Sheffield, particularly given increasing automation in the workplace.

“UBI has the potential to be a bold, radical change to how our economy and society works with benefits for people’s wellbeing and how we support people in need,” she said. “In order to face up to these realities, I think it is completely right that radical solutions are considered.

“As a council, we are getting behind this and committing to looking at this further and working with a Labour government in trialling this.”

Sam Walby, a co-founder of UBI Lab Sheffield, said: “It’s an idea whose time has come. It seems to have been included in a lot of new visions, whether that’s for politicians or political writers.

“There seems to be a common theme that’s running through, which is, ‘how do we reimagine the welfare state for the 21st century?’

“We’re not saying this is a silver bullet that could solve everything, but we need to be exploring it. Some of its results might be completely surprising and unexpected.”

The cost of any future Sheffield pilot would be met entirely by an external funder, likely a national government, and not Sheffield city council, UBI Lab Sheffield said.

McDonnell confirmed earlier this year that such funding could come from a future Labour government.

“I would like Liverpool – of course I would, I’m a Scouser – but Sheffield have really worked hard. I’ve been involved in their anti-poverty campaign and they’ve done a lot round the real living wage,” he said.

Olivia Blake, the deputy leader of Sheffield city council, said she had invited McDonnell up to the city to “discuss these radical proposals further”.

Jason Leman, the chair of UBI Lab Sheffield, said the city was uniquely predisposed to hold a pilot due to its geography.

“It’s like a collection of towns, it isn’t a monolithic city. Every city has its neighbourhoods but Sheffield is particularly divided. There’s a real disparity between the north-east and the south-west in terms of wealth, life expectancy and life experience,” he said. “Within Sheffield’s districts, you have communities that are almost self-supporting.”

UBI Lab will attempt to gather the support of organisations across the city, including both universities, the local NHS branch and small businesses, encouraging them to sign a pledge of support for the pilot.