The idea is one of a number put forward in a report by Changing London aimed at influencing the policy of the next mayor of London, in order to improve the capital for children and young people.
It calls for the introduction of "London Sundays", whereby children under the age of 18, and an accompanying adult, get free tube travel and access to cultural institutions in the capital.
Currently only children under the age of 11 are eligible for free tube travel.
Other ideas include a ban on advertisement near schools so children are not subject to commercial pressure, the appointment of a London Young Mayor to campaign on youth issues, and the creation of a London Child Trust so all children in the city have savings when they enter adulthood.
Some of the ideas were sourced from cities abroad, while others were gathered from Londoners through the Changing London website.
David Robinson, co-founder of Changing London, said: “London is a wonderful city, diverse, rich and full of talents but it is not the best that it could be.
“The next London mayor must listen to the views of Londoners and take bold steps to make their ambitious visions a reality."
The next mayoral election is due to take place in 2016.
Last week the London Evening Standard reported that Tottenham MP David Lammy, who is seeking to be nominated as Labour's mayoral candidate, said 1,000 roads across London should be turned into play streets at certain times to improve community relations and provide a safe area for children.
