Remove and discard the watercress stalks and roughly chop the leaves.
Melt the butter in a saucepan over a medium heat. Add the onion and cook until tender, about 5 minutes. Stir in the potato, milk and stock and bring to the boil. Reduce the heat and simmer until potatoes are tender about 15 to 20 minutes.
Add the fresh watercress and blend the soup with a food processor or using a handheld liquidiser until smooth. Press through a sieve if desired. Stir in the single cream and season with salt and pepper. Ladle into warmed bowls and serve.