Smoking could be banned in Trafalgar and Parliament squares and London parks if a report by the city's Health Commission is implemented.
Other suggestions include Oyster card discounts for commuters who walk part of the way to work.
Smokers' group Forest said the call for a smoking ban was "outrageous". Boris Johnson it could be considered if "it would actually save lives".
The government said it had no plans to ban smoking in public places.
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.
'Beacon of health'
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.
The report's recommendations also include:
- Traffic light labelling on menus at restaurant chains with more than 15 outlets
- Planning guidance to prevent new junk food outlets opening within 400m (1,300ft) of schools
- A minimum 50p per unit price for alcohol in boroughs affected by problem drinking
- An acceleration of measures to reduce air pollution in the capital.
Lord Darzi told the BBC he would like parks to be a "beacon of health".
"London should lead the way for Britain, and the mayor should lead the way for London by acting to make our public spaces smoke free," he said.
Speaking on BBC Radio 4's Today programme, Lord Darzi said: "We want to make sure kids are out there exercising rather than looking at adults smoking in the corner."
At the scene
In Trafalgar Square there are mixed feelings about a ban.
Robin Mason, 68, from Oxford, says it's a "waste of money".
"The government should not be spending £6.5m on a ban that would be so hard to enforce," he says.
His opinion is echoed by 21-year-old smoker Domica Perfect who thinks the ban is "a load of rubbish".
"I don't think it really matters because we're outside in the open so it's not like people are forced to breathe in your smoke," she says.
French student Matthieu Osmond, visiting London on holiday, says: "Personally I don't like smoking or the smell but outside I don't have a problem with it."
But retired teacher Kathleen Barnsley, from Wakefield, says: "It would be an absolutely brilliant idea.
"The problem that occurred when they banned smoking inside is that it brought everyone outside so children now see lots of people smoking and it sets an awful example."
Boris Johnson, the Mayor of London, said: " If we were to consider a ban on smoking in parks, we would need pretty clear evidence that this would have direct health benefits - in other words, that it would actually save lives."
The Chief Medical Officer for England, Prof Sally Davies said: "I welcome any measures to reduce both active smoking and its role modelling in front of children."
However, Prof Robert West, director of tobacco studies at University College London, said the plan "tests the limits of how far it is reasonable to limit the freedoms of some members of society in what is seen as a good cause", but he admitted it could save lives.
Simon Clark, director of Forest, said: "A ban on smoking in parks and squares would be outrageous.
"There's no health risk to anyone other than the smoker. If you don't like the smell, walk away.
"Tobacco is a legal product. If the Chief Medical Officer doesn't like people smoking in front of children she should lobby the government to introduce designated smoking rooms in pubs and clubs so adults can smoke inside in comfort.
"The next thing you know we'll be banned from smoking in our own gardens in case a whiff of smoke travels over the fence."
In 2011, New York introduced a ban on smoking in Central Park and all of the city's parks and beaches.