Five to 10-year-olds travel free on Transport for London (TfL) services, which run mainly north of the Thames, but in the south most rail services are not TFL-run and require tickets.
London Assembly member Val Shawcross called for the scheme to apply on all public transport, initially in August.
The Rail Delivery Group says a savings card is available but it would consider working on such a scheme.
Ms Shawcross, Labour member, said introducing the idea initially as a summer pilot would be a good use of transport services when passenger numbers dip.
As an example, she said that currently a child's peak return ticket from Orpington, south London, in Zone 6 to Charing Cross costs Â£6.80, while a similar service north of the river from Rainham, also in Zone 6, is free.
She said: "We want the mayor to take a look at it, and although we don't run the rail services in London, which has been part of the issue, TfL does have a good working relationship and we have an Oyster card and Freedom Pass system for the whole of London.
"This would not only help millions of families but also undo the current north-south divide which means that children living in vast areas south of the river are effectively excluded from getting free travel."
The Rail Delivery Group, which represents train operators and Network Rail, said: "Although not free, 5-10 year old Zip card holders can make off-peak train journeys in London for a flat fare of just 75p, capped at Â£1.50.
"Operators would work with the Mayor, the London Assembly and the Department for Transport if a free travel scheme was something they wished to introduce."
An online petition with the same aim has gained 300 signatures.
"It is really important for children to grow up with the notion that public transport is a good option," one woman who signed it said.
Children in London face a north-south transport divide, a politician says.