George Osborne avoided official channels and Department for Transport oversight to offer the London mayor, Boris Johnson, funding for the garden bridge scheme, parliament’s spending watchdog has found, warning the project may not have been approved if the normal processes had been followed.

The National Audit Office said the public money being poured into the £175m Thames bridge is at greater risk than the private funds, and a “high degree of uncertainty” hangs over the scheme’s value for money.

The chancellor’s unilateral decision to commit public funds to kickstart fundraising is described in a letter from the NAO to MPs as unorthodox. A total of £60m of public money has been granted to the project, whose chief cheerleader is actor Joanna Lumley.

Sir Amyas Morse, of the National Audit Office, said of the project: “It is important to note that the results would not in normal circumstances suggest a compelling value for money case ... The department’s own quantitative analysis suggested that there may or may not be a net benefit and, especially once concerns over deliverability were taken account of, the project might well not have met the department’s normal threshold for allocating its finite funds.

“In this context it is important to recognise the wider context, particularly: the initial funding commitments were made by the chancellor to the mayor of London, without the DfT’s involvement.”

The letter added: “The garden bridge is expected to be predominantly financed through private donations. However, public money was transferred at an early stage in order to allow expenditure on pre-contract award activities with a view to kickstarting fundraising efforts. While this rationale is clear, the timing puts the public sector … at a higher risk than private finance sources of funding proving abortive.”

George Osborne and Boris Johnson Photograph: Stefan Rousseau/PA

The watchdog’s verdict emerged alongside fresh questions over precisely how much has been raised by the private sector towards the bridge. On Wednesday, the Garden Bridge Trust announced Sky had offered £5m to the project, making a total of £85m in pledges from private sources. The £85m was, however, cited by the trust two months ago, prompting accusations of a lack of transparency over the true level of private funding.

Michal Ball of campaign group Thames Central Open Spaces said: “It seems as if Sky was already a previously undisclosed donor given the private investment amount has not gone up since last autumn.”

Bee Emmott, executive director of the trust said: “The garden bridge is making huge progress and construction will start in the summer. We have a robust business case and we are confident we will reach our targets.”

Elsewhere, scrutiny has been growing over a series of meetings held by Johnson, one involving the bridge’s designer, Thomas Heatherwick, on 1 February 2013, two weeks before Transport for London invited Heatherwick Studio to tender successfully for the project. The meeting, though, was omitted from the mayor’s official report to the Greater London Assembly despite the inclusion of his main activities being a statutory requirement.

Critics also asked questions over a mysterious trip by Johnson to San Francisco in early 2013. Although the mayor admits the trip related to the garden bridge he has refused to provide any further detail and, again, also omitted the excursion in his monthly report to the London Assembly.

The NAO provided its damning judgment after Meg Hillier, chair of the public accounts select committee, had asked it to examine the DfT’s rationale in providing £30m for the project, matching £30m from Transport for London. It found that the money had been agreed because the chancellor had already promised it. However, the NAO reported that “should the project fail, the department is at risk of having obtained no substantial benefits in return for its grant”.

Gareth Thomas, MP for Harrow West, on Friday called on Osborne to justify the use of public cash on a “vanity project”. He said: “At a time of deep public sector cuts, this money could have been spent on countless other projects where the business case has already been proved.”

Lib Dem mayoral candidate, Caroline Pidgeon, said: “It is incredible that, while the real benefits of the garden bridge are hard to quantify, George Osborne didn’t hesitate to instruct both the Department for Transport and the Mayor of London to pour taxpayers’ money into the scheme.”

In correspondence relating to the bridge, previously released under the Freedom of Information Act, it has been revealed that Osborne encouraged the mayor of London to support the plan for an “iconic” new bridge. Lumley, a longstanding friend of Johnson who has been a vocal champion for the bridge between Temple and the South Bank, also lobbied in 2012 for Johnson to meet her and Heatherwick. She is now a trustee on the Garden Bridge Trust, the charity that will maintain the river crossing if and when it is built.

Opponents say cyclists will have to push their bikes across the bridge, which will be shut every night and once a month during the day for corporate fundraising events.