According to the mayor's office, London has one of the highest child overweight and obesity rates in Europe, with nearly 40% of children aged 10 and 11 overweight or obese - something that Khan believes is a "scandal".
"It can't be right that, in a city as prosperous as London, where you live and the income you have can have a massive impact on whether you have access to healthy, nutritious food and your exposure to junk food advertising".
'That is why I'm proposing to ban adverts for harmful junk food from our entire Tube and bus network.
City Hall issued a statement from Mayor Sadiq Khan on Friday, announcing the new measure and that he expects feedback before it is actually implemented.
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In welcoming the proposal, Cox said Cancer Research UK wants to see a national "ban on junk food TV adverts before 9pm in the upcoming obesity strategy so that more young people can be protected from the marketing tactics used by the food industry". He also cited similar advertising rules introduced in Amsterdam as a successful step towards combating obesity.
Khan unveiled his proposal to rid the city of banners and bus ads that promote "unhealthy food and drink" this week, striking the images from the London Underground and other public places.
Ms May has been fiercely criticised, including by celebrity chef Jamie Oliver who said the action had been gutted after she "took over and pushed it out".
Food and drink advertising contributed around 20 million pounds ($27 million) to Transport for London's revenue during the 2016-17 financial year.
"The increase of obesity in the United Kingdom is multidimensional, aspects of which include socioeconomic status, physical inactivity as well as what we eat, how much we eat and when we eat".