In a large saucepan, mix the water, potatoes, carrots, celery, onions, salt and pepper. Bring to boil. Reduce heat and simmer 30 minutes, or until vegetables are tender.
Mix the ham into the vegetable mixture.
In a medium saucepan, melt the butter. Stir in the flour until smooth. Slowly pour in the milk. Bring to a boil. Cook and stir 2 minutes, or until thickened. Stir in the Cheddar cheese until melted.
Mix the melted cheese mixture with the vegetable mixture and serve.
