You get specialist aluminium polish thay can do wonders when used with a proper polishing wheel etc.
Britemax twins are great for aluminium and other metals.
If you want a cheap home solution you can fill a pot with boiling water, and add vinegar in a 1:2 ratio with water, leave part in to soak. Finally, you can polish it up with a toothbrush or small vikan brush, and either white vinegar, or ketchup and the mild acidity will remove the oxidisation.