Vir osol (Clover) is great on body fats too .
What you might find is that you might need some thing with a bit of limescale removal as well , where the fats oils and greases are locked in with the lime scale (depending on how hard your water is)
STC or Scale it (clover)both hit body fats and lime scale in one go safe on chrome etc. too.
Always worked very well and quickly for me
T