The Labour MP Dame Margaret Hodge has been found to have breached the MPs' code of conduct during her review of the Garden Bridge project.
The Garden Bridge Trust was established in 2013 to build a tree-lined bridge across London's River Thames.
But the charity announced in August it was winding up after the project, which received £37m of public money, was abandoned.
The project was conceived under the previous London mayor, Boris Johnson.
Sadiq Khan, the city's current mayor, reviewed the scheme in 2016 to see if it offered value for money for taxpayers.
The Greater London Authority commissioned Hodge, who has been MP for Barking since 1994, to undertake the review free of charge.
But the GLA paid Hodge £9,500 when she completed her review, which recommended that the scheme should be scrapped.
Hodge used her parliamentary office for 20 meetings and used House of Commons stationery for her review, an investigation found.
Kathryn Hudson, parliamentary commissioner for standards, upheld a complaint by Andrew Boff, a Conservative London Assembly member, that Hodge used her parliamentary office and Commons stationery to undertake paid work.
Hudson's report, published yesterday, said Hodge initially expected to spend one day a week on the review for three months and did not regard it as "wholly separate" from her parliamentary duties.
In written comments to Hudson in October, Hodge said the review, which led to the abandonment of the bridge project, took more time than expected and there was an unclear distinction between "separating activity in support of parliamentary duties from activity arising from parliamentary duties".
She added: "if the committee finds that I was in breach of the rules I will of course offer a fulsome apology and will pay back the £3 that could have been spent on headed paper."
Hudson's report concluded: "I am satisfied that Dame Margaret was not motivated by financial gain, but she has, nonetheless, as a result of these events accrued a financial benefit while using House resources and House-provided resources were used to the benefit of the GLA."
After the verdict, Hodge said in a statement: "I am extremely sorry that I inadvertently breached parliamentary rules. I carried out this inquiry in good faith and in the public interest. I think all MPs would benefit from greater clarity in the rules governing the use of offices."
Boff said the verdict left a "sour taste", adding: "Sadiq Khan has paid his friend Dame Margaret Hodge £9,500 of taxpayers’ money to conduct a review in which she committed a serious breach of the parliamentary code of conduct.
"She is an MP of more than 20 years’ experience and a former chair of the Public Accounts Committee, so it seems hard to believe she was unaware of the rules.
"An honourable politician would consider compensating the taxpayer for the costs she avoided by using parliamentary resources for free. Instead she has offered a dismissive £3."