Where Winston Churchill was taught to break up ploughed land (6)
I believe the answer is:
harrow
This clue is a double definition.
'where winston churchill was taught' is the first definition.
(English public school)
'to break up ploughed land' is the second definition.
(Other definitions for harrow that I've seen before include "Soil cultivator - English public school" , "Till" , "Distress greatly - public school" , "Break new ground" , "Cultivator that pulverizes or smooths soil" .)