In favour of church showing influence (5)
I believe the answer is:
force
'influence' is the definition.
(force is a kind of influence)
'in favour of church' is the wordplay.
'in favour of' becomes 'for' (I've seen this before).
'church' becomes 'ce' (abbreviation for Church of England).
'for'+'ce'='FORCE'
'showing' acts as a link.
(Other definitions for force that I've seen before include "Impel, coerce" , "Impetus" , "Northern waterfall" , "Energy" , "Physical coercion" .)