Development of the Thomas Heatherwick-designed Garden Bridge in London is set to continue after a crucial breakthrough was reached over public funding allocated to the project.

Progress on the £175m (US$294m, €216m) development of the tree-lined river crossing had stalled following a row between the Garden Bridge Trust and Lambeth Council over the £30m (US$46m, €42m) contribution being paid by Transport for London (TfL) – the local government body responsible for the city's transport network.

However, a new agreement has been reached allowing work to go ahead on the condition that this funding is slashed by two thirds. Negotiations are now due to resume over the development of the bridge’s south landing site.

Lambeth Council leader Lib Peck said: “I’m pleased that Londoners are getting a better financial deal particularly at a time of austerity when all public sector organisations are being forced to make deep cuts to services.

“We’ve been in tough negotiations with the Garden Bridge Trust and Transport for London and I’m pleased we’ve successfully agreed a deal that will cut London taxpayers’ contribution towards the Garden Bridge by two thirds.”

Chair of the Garden Bridge Trust, Lord Mervyn Davies said: “We are delighted to move forward with the project. We have been hugely successful in our efforts to raise funds from the private sector, with £85m (US$131m, €119m) pledged to date, and we have agreed that any of the committed funds from TfL spent over the £10 million will be treated as a loan.”

Since it received final approval in December 2014 – when London Mayor Boris Johnson described it as “a stunning oasis of tranquillity in the heart of our city” – the Garden Bridge has drawn criticism for both its price tag and unusual design.

However, the project has been defended by several high-profile architects, including Richard Rogers. In a letter to London’s Evening Standard newspaper, he wrote: “We should not be criticising the Garden Bridge but celebrating it for what it is – a jewel of public space, a vital new connection for pedestrians and an oasis at the heart of the city.

“This is the most valuable new piece of transport infrastructure for London. Please don’t confuse this with the fact that it has a garden on it.”