There is more than one artist with this name: 1) Fluffy is an all-girl British indie punk/pop band from London. Formed in 1994. Lineup: Amanda Rootes - Vocals/Guitar, Angie Adams - Drums, Bridget Jones - Guitar, Helen Storer - Bass.
Musically they were often described as a "messy" Elastica. In fact, one member admitted during an interview that they would often listen to Elastica while cleaning their flat because the music was so "clean" to them.

Read more about Fluffy on Last.fm.