Reportedly influenced band (5)
I believe the answer is:
suede
'band' is the definition.
(British band)
'reportedly influenced' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'influenced' becomes 'swayed' (swaying is a kind of influencing).
'swayed' sounds like 'SUEDE'.
(Other definitions for suede that I've seen before include "Hide from kids" , "Fabric" , "Leather with a soft napped surface" , "Undressed kidskin" , "Undressed leather" .)