The shooting of foxes with a shotgun is a skill learnt through practice-Let me explain.
The need for heavy shot or not relies on the position of the fox when shot .A fox squeaked in will usually come face on,not showing the whole body,therefore heavy shot is needed to transfer enough energy to the vital organs to kill it .Like p@g said, BB is the shot for this .However,If your lucky enough to be invited on a days driven fox shooting then its different .When a fox runs ,or anything else for that matter ,its vital organs are usually side on and very vulnerable.As long as marksmenship is good th