I neglected to mention child fares for London transport – not a topic that I find particularly thrilling, and it’s also rather complex. The official are available details here.
My quick summary:
Under 11: free on bus and tube (must be with paying adult); child fare on National rail trains, which is reduced if the child uses a 5-10 Oyster photocard
11 – 15: child rates on bus, tube, and trains. If the child has an 11-15 Oyster photocard – buses are free and tube / train fares are further reduced.
16 – 17: adult rate. If with 16+ Oyster photocard – buses, tube, and some National Rail services are half the adult half the adult fare.
On travelling with the wee wee ones: If your child needs a stroller, pram, buggy – be aware of two unpleasantries that you could encounter:
a) Lots and lots of stairs, and/or long escalators (with fast-moving Londoners walking up or down on the left). It’s the only way out of many many tube stations. A whole guide book is available here.
b) Mayhem on the Tube/bus/train. If you attempt to travel during commuting times, you may find it impossible to fit a buggy on. I’ve done this, and would not recommend it to anyone else. Better to leave the stroller at home and carry your little angel (if that’s an option).