The letter to Lord Mervyn Davies stated that the continuation of the project would expose London taxpayers to additional financial risk from the bridge’s construction, operation and maintenance.
The decision was made after Dame Margaret Hodge’s independent review into the Garden Bridge project, which was analysed by the mayor of London.
Mr Khan said: “Under the previous mayor, a considerable amount of London taxpayers’ money has already been spent on the Garden Bridge.
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“I have always been clear that not a penny more of taxpayers' money should be allocated to the project.
“With planning permission due to expire this year, many outstanding issues remain, including spiralling construction costs and doubts around funding the maintenance of the bridge.”
The funding gap has now been recorded at over £70m and Mr Khan has said that it is unlikely that the trust will raise the private funds required for the project.
“I am simply not prepared to risk a situation where the taxpayer has to step in and contribute significant additional amounts to ensure the project is completed,” he added.