I have the prettiest stainless steel stove top kettle but it's gotten all filthy from grease and grime from it's close proximity to saucepans, etc. It doesn't fit in the dishwasher so this grime is accumulating making it look a lot less pretty.

I have tried washing it with detergent, cleaning with sugar soap, and polishing with eucalyptus and tea tree oil but so far this has only worked on the top half leaving the bottom half with a dirty, mottled look. I assume this is something to do with the heat solidifying the grease.

Please does anyone have a remedy that will work, bearing in mind that I am a tea addict and use my kettle almost constantly so I can't soak it for hours or anything like that.