Heat olive oil in a large pot over medium heat. Add celery, onion, carrots, basil, garlic, and black pepper until tender, about 10 minutes. Transfer 1/2 vegetable mixture to a food processor.

Drain 1 can stewed tomatoes; add to the food processor; pulse until smooth. Stir mixture into pot.

Stir remaining 2 cans stewed tomatoes, clams, clam juice, and potatoes into pot; bring to a boil. Reduce heat and simmer soup until heated through, 15 to 20 minutes. Season soup with Worcestershire sauce.