Speaking during Mayor's Question Time Mr Khan said scrapping the scheme, which is due to be completed in 2018, would "simply cost Londoners more to cancel the project" than it would to finish building the bridge.
With over £60m of taxpayers money pledged towards the scheme, £37.7m has already been spent by the Garden Bridge Trust.
By cancelling the scheme, this money would be lost in full with "no benefit at all for Londoners or taxpayers".
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Both Transport for London (TfL) and the Government have committed £30m each to the project, with the remainder to be raised through private donation.
In addition, £20m of TfL's pledge is in the form of a loan to be repaid in full.
If the bridge is built, not only will TfL be repaid its £20 million loan, but it will also pay approximately £22m in VAT to the Treasury, resulting in the overall bill to taxpayers for completing the bridge will be £18m, less than half the cost of cancelling the project.
Mayor Khan said: "From the point at which I became Mayor, it was quite clearly in London taxpayers' financial interest to complete the Garden Bridge project.
"If the Bridge was cancelled now taxpayers will have spent £37.7 million for no benefit at all. However if we complete the project and our loan is repaid in full then the ultimate cost to taxpayers will be under half that cost at £18 million.
"So I will support the building of the Garden Bridge, but I am demanding that the project is made more accessible and open to all Londoners in return."
(LM/CD)
