Smoking could be banned in Trafalgar and Parliament squares as well as the city's parks if a report by London's Health Commission is implemented.
Other measures put forward include Oyster card discounts for commuters who walk part of the way to work, and a ban on junk food shops near schools.
There should also be traffic light labelling on menus at restaurant chains with more than 15 outlets, it says.
Smokers' group Forest labelled the call for a smoking ban "outrageous".
The report, called "Better Health for London", has been put together by former health minister and cancer surgeon Lord Ara Darzi.
In it he claims half of all adults in London are obese or overweight and the city now has more obese and overweight people than New York, Sydney, Sao Paolo, Madrid, Toronto and Paris.
About 1.2 million Londoners smoke, and the commission claims 67 school children take up the habit every day.
The smoke free plan would see the mayor use his by-law powers over Trafalgar Square and Parliament Square and his influence over the Royal Parks, the board of which he appoints.
Local councils could pass similar by-laws for their parks and open spaces.
The implementation of the scheme has an estimated cost of £6.5m over five years
