Just found this on TFLs website after a more in-depth search:
“Travelling with children
Up to 10-years-old
Children aged 10 years or under can travel free on buses and trams whether or not they are accompanied by an adult. They can also travel free on Tube, DLR and London Overground services at any time as long as they are accompanied by an adult using a Visitor Oyster card or a valid ticket *.”
So, looks like they are free if me and t’wife buy a travelcard…..