Mr Khan has written to Michael Gove, the secretary of state for environment, food and rural affairs, setting out his demands.
The mayor has requested powers in regulating non-road mobile machinery, river and canal emissions, and wood and solid fuel burning.
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Mr Khan said: “Non-transport sources contribute half of the deadly emissions in London, so we need a hard-hitting plan of action to combat them, similar to moves I am taking to reduce pollution from road vehicles.”
Non-road mobile machinery (NRMM) such as diggers and bulldozers are the second-largest source of ultra-fine particulate matter (PM2.5) emissions in London and the fifth-largest source of oxides of Nitrogen (NOx).
Mr Khan has requested that he receives greater powers to enforce the standards of the Non-Road Mobile Machinery Low Emission Zone (NRMM LEZ).
This scheme imposes minimum emissions standards for machinery used on construction sites.
Mr Khan added: “With more than 400 schools located in areas exceeding legal pollution levels, and such significant health impacts on our most vulnerable communities, we cannot wait any longer and I am calling on government to provide the capital with the necessary powers to effectively tackle harmful emissions from a variety of sources.”