Scrub mussels in cool water and pull off beards; discard any whose shells don't close when tapped. In an 8- to 10-quart pan, combine mussels and wine; bring to a boil over high heat. Cover and simmer over medium heat until mussels open, 5 to 8 minutes. Pour into a colander set in a large bowl to collect juices. Let mussels stand until cool enough to touch.
Meanwhile, peel potatoes and cut into 1/2-inch cubes. Peel and chop onion. Rinse celery and cut into 1/2-inch pieces.
In the pan used for mussels, melt butter over medium heat. Add onion and celery; stir often until onion is limp, 6 to 8 minutes. Add curry powder and basil; stir until spices become more fragrant, about 30 seconds.
Pour mussel juices from bowl into pan. Add tomato sauce, cream, and potatoes. Turn heat to high; when mixture is boiling, cover, reduce heat to low, and simmer, stirring occasionally, until flavors are well blended, about 30 minutes.
Meanwhile, remove mussels from shells; discard shells.
Add mussels to soup; cover and simmer just until mussels are hot, 3 to 5 minutes. Add salt and pepper to taste. Ladle into bowls.