Disclaimer: haven't ridden this yet. Well, bits of it.

Using a well trodden backstreets route from SE25 to central Croydon, then various minor roads to get over towards Farthing Down / Happy Valley / Chaldon.

Might be a less direct although more family friendly way out of town than the "Avenue Verte" (NCN20 which uses a busy "B" road through Woodmansterne), and easier terrain than the NCN21 south of New Addington.

Maybe a good way to access the Bletchingley - Outwood - Wivelsfield L2B route...