Most cost effective way of travelling between zones 1-3 in london

Grumpy_chap

WagathaChristie said:

the cheapest way to travel around London.

I live in zone 3 and work in zone 1. 

You probably need to be more precise on where and where.
Zone 3 to Zone 1 can be as close as Herne Hill to Elephant & Castle, so only three miles which is most cheaply covered on foot and probably pretty much as quick as any other mode of transport.
Alternative end points could be entirely different.