Not so helpful: "Children under the age of 11 can travel for free on the TfL» network between Reading and London Paddington with a fare-paying adult, making day trips to the capital even more affordable. Under TfL rules, all children under the age of five can travel for free with a fare-paying adult."
Not that I have any children, but the contradiction puzzles me.
Marlburian
I think for an explanation you have to look up TfL's
rules for 5-10 Zip Oyster▸ photocards:
Children aged 5-10 get free travel on all our transport services with a Zip Oyster photocard.
Benefits
Free travel on Tube, DLR▸ , London Overground and TfL Rail
Free travel on most National Rail services that accept pay as you go
50% off adult rate tickets on the Thames Clippers River Bus services
Pay as you go at a child rate on the Emirates Air Line
Who is it for?
Children aged 5-10 can use a 5-10 Zip Oyster photocard.
Your child doesn't need a photocard to:
Travel free on buses and trams
Buy child-rate paper tickets (unless they look older than 10)
Travel accompanied by an adult on Tube, DLR, London Overground, TfL Rail and some National Rail services
How to apply
A parent or guardian must apply for a 5-10 Zip Oyster photocard.
Under-5s always travel free, and "accompanied" is left unsaid.
You'll note the less than helpful "
some National Rail services" there. In fact, having read that, I'm still not clear what free travel with no card is based on.