Place water in a large saucepan, bring to the boil and add the turnip, stock cube and stock granules. Lower the heat and simmer for 10 minutes.
Add the celery, leeks and onions and simmer for a further 15 minutes.
Remove from the heat and allow to cool slightly. Add the tarragon, then blend in a food processor, with a hand-held blender, or simply mash a little with a wooden spoon or potato masher for the desired consistency.
Reheat, if using a food processor, then divide into warmed soup bowls and serve.