New edinburgh clam chowder

Name: New edinburgh clam chowder
Ingredients: 1 rasher of bacon; 1 medium carrot, thinly sliced; 1/2 an onion, chopped; 1 stalk of celery, thinly sliced; 3 medium-sized floury potatoes, peeled and diced; 2 Tbsp of butter; 2 Tbsp of flour; 300ml of light cream; 2 dozen Otago clams (cockles), either self-gathered from the many laces where they may be found around Dunedin, or bought live. (A 425 g tin of clams is a less messy alternative but don't expect them to taste as good).; 1 tsp wine vinegar; salt and ground black pepper to taste; pinch of smoked paprika (optional)