What I have found with the white leather is that those "dirty" areas are usually where the color has worn off, and if you try to clean it, it will make it worse. However :0), there is help! Get some of the dab on white shoe polish. Dab it on, let it dry, then buff. It might take several dabs depending on how bad the spot is, but I have rehabbed whole bags this way. It will need touching up occasionally. I think if you have white leather anything it is good to have the polish on hand.
Hope this helps.