The future of Thomas Heatherwick's Garden Bridge has been thrown into question again, after it emerged that costs could rise well above the estimated £185 million, and that the charity behind the project is at threat of liquidation.

The proposed bridge across London's River Thames has faced numerous obstacles over the past two years, but its stated price tag has only ever increased by £10 million.

But Garden Bridge Trust chairman Mervyn Davies has now admitted that the final cost could be far higher – placing the entire project in jeopardy.

In accounts filed at Companies House, Davies said: "The last external estimate of the total project cost of the Garden Bridge was £185 million but, due to the hurdles still to be cleared and the ensuing delays, the final cost could substantially exceed the formal estimate."

The accounts also reveal that the Garden Bridge Trust is no longer a "going concern", meaning its finances are subject to collapse.

The charity will only survive if it overcomes several issues, which include securing rights to land on both sides of the river, and getting final sign off from London mayor Sadiq Khan – who is more sceptical of the project than previous mayor Boris Johnson.

"It is hoped that these [risks] will be resolved over the months ahead, but since a number of these matters are outside the control of the trustees, they recognise that, if this is not possible, they will need to consider the further delay to the project and, in a worst case scenario, whether the project remains viable," reads the report.

Originally conceived by British actress Joanna Lumley, the 367-metre-long Garden Bridge is proposed between Temple and the South Bank.

London designer Thomas Heatherwick drew up the plans, which include full-size trees and planting beds along the deck, and a "super-strength" copper-nickel skin covering the structure's underside and legs.

The project has been granted £60 million of funding from the UK government's transport departments, with £20 million of that being treated as a loan. Around £40 million of this has already been spent.

The trust has to raise the rest of the £185 million or more through private donations. Davies claims that it has so far secured a further £69 million – just over half the required amount – but he is confident that it can find the rest.

The report makes reference to an updated fundraising strategy, developed in response to the challenges already faced.

"Given the success we have had so far, we are confident that we will meet our funding targets," said Davies.

The Garden Bridge has been mired in controversy over the past two years. Questions were raised over the procurement process for the design of the bridge, with some believing Heatherwick was given an unfair advantage during the bid process.

Access to the bridge has also caused issues, with campaigners protesting against lack of bicycle access and the fact that the structure will be closed to the public at night and for 12 days each year.

The project is currently the subject of a formal review, ordered by Sadiq Khan to assess whether the project provides value for money. The results are expected in March 2017, and the trust has paused fundraising until after then.

If the report concludes that the bridge doesn't offer value to the taxpayer, it could prompt Khan to reconsider his support for the project – another move that could prove crippling.