You need to make sure the boots are completely dry first. Stuff them with newspaper and leave them in the airing cupboard for a day or two. Then, with a soft brush, get rid of the white marks (they should brush off easily) and use a good quality solid polish (not a liquid self-shining one) like Cherry Blossom or Kiwi.
when they are dry, brush off what you can - dab the white marks with some white vinegar - leave to dry and then polish - if you don't use vinegar (or lemon juice), the whire marks will reappear through the polish.