The leader of Lambeth Council has criticised the use of public funds for the proposed Garden Bridge.
The Lambeth Labour leader casts doubt on the claimed transport benefits of the bridge.
"No matter whether you're for or against, it is difficult to justify Transport for London (TfL) funding the project to the tune of £30 million," wrote Cllr Peck.
"The Mayor characterises the bridge as a transport scheme in order to raid TfL's coffers. The bridge may do many things, but how can it be argued it will significantly boost walking? It is in the wrong place for that, sandwiched between two other crossings.
"And as cyclists will be banned, it will do nothing to get people out of their cars and onto bikes.
"So while it might have other merits, it is surely wrong for TfL to issue a blank cheque, particularly given the financial pressures they face from the Chancellor."
Cllr Peck also addresses the issue of the Lambeth-owned land on the South Bank where the Garden Bridge's southern landing would be built.
"Over the next few months, I need to be convinced that Lambeth residents will be advantaged, not disadvantaged, by the renegotiation.
"The Mayor's £30 million contribution from the public purse will be uppermost in my mind.
"It is true that Lambeth could pull the plug on the project now by refusing to enter into negotiations. But that feels very alien to a Lambeth that has increasingly played a bigger role in shaping our city.
"London is an ambitious city, known for giving space to big ideas and creative projects. Lambeth spent far too many years in the past being known as the place where such ambitions were blocked rather than realised.
"The Garden Bridge is a creative idea but I am clear it can not come at any cost.
"A trick has been missed on its location, and with a more flexible approach by the Garden Bridge Trust an alternative could have been found."
Cllr Peck's intervention comes after Transport for London boss Sir Peter Hendy ordered a review of the process that led to Heatherwick Studio and Arup being selected to design the bridge.
In a letter to Lib Dem Caroline Pidgeon AM, Sir Peter wrote: "In response to your letter and the general level of interest in the Garden Bridge, I have instructed a review of the overall process of procurement of the Garden Bridge design contracts, the findings of which I will publish in full."
Caroline Pidgeon said: "Peter Hendy's decision is especially welcome as Boris Johnson has so far blocked any attempt to undertake a review.
"Hopefully the review will be thorough and answer all the remaining questions over the procurement process. Most importantly it should lead to lessons being learnt for the future, including the need for future projects of this significance being always open to a proper design competition."
Meanwhile Lambeth's sole Green Party councillor Scott Ainslie has also registered his objection to the proposal to allow the Garden Bridge Trust to use council-owned land on the South Bank.
Cllr Ainslie said: "It's deplorable that land, which was given to Lambeth for public use, and is currently protected, would be lost to commercial buildings in an area where public open green space is scarce and precious."
He added: "This land and pedestrian access was created at public expense in the late 1980s and was passed to Lambeth as a custodian – to ensure it remained as open space for future generations. By proposing such a fundamental change in the terms on which the land was passed to the borough, Lambeth is giving away the people's family silver.
"Instead it should be protecting a precious and scarce resource currently enjoyed by many thousands of residents and visitors.
"If the Garden Bridge goes ahead this land will no longer be accessible to groups bigger than 8 without advance booking, nor to any of the public at night, nor when the bridge is closed to the public for private functions."
The Garden Bridge Trust is currently holding a series of consultation events on its proposals for managing the construction of the bridge. The third and final drop-in event is on Monday 29 June at Waterloo Action Centre.
In a statement, the Garden Bridge Trust said: "We welcome scrutiny by local authorities and continue to engage with them on a regular basis, meeting Cllr Peck again this month, and we are currently undertaking a consultation exercise seeking the community's views on our construction plans.
"The bridge's public funding is helping unlock £115 million of private money, with more than £67 million already raised from businesses, charitable trusts and individuals.
"This money will produce a real asset for Londoners, securing economic benefits on both sides of the Thames.
"We have a robust, fully scrutinised plan to cover operational and maintenance costs through private funding, that is subject to annual review, and have set out our schedule which will see building begin in early 2016 and complete in summer 2018.
"The bridge's location was chosen following detailed studies by Transport for London, providing a stunning new landmark for London, a new crossing for pedestrians in the heart of London, improving connections for as many as 10,000 commuters a day, and an amazing garden for Londoners, and the people of Lambeth and Westminster."