Or you could go 1 stop on a bus for £1.50 and only pay the fare if you were not using other buses around then
Talking of which, I have tried to look up a fare from Catford to Catford Bridge without success
A good one I unearthed is Harrow & Wealdstone to Harrow-on-the-Hill, £5.90 single or £11,80 return via Queen's Park and London Marylebone.
Also, Greenford to South Ruislip via West Ealing, to avoid the Central Line direct. Various fares between £5.50 and £23.30 came up. The £22.30 fare involves changing at West Ealing, Paddington, Marylebone and Gerrards Cross.