Slowly melt the butter in a medium saucepan with the fennel seeds and bay leaves. Add all the vegetables, turn up the heat a little, then sweat them with the lid on, stirring occasionally, until they are soft but not coloured. This should take about 20 minutes. Season the vegetables well. Add the wine, replace the lid and simmer until the potatoes are just cooked (another 5–6 minutes or so).
Meanwhile, cut up the fish into good mouthful-sized chunks. In the pollock you may find a row of short pin bones between the fillet and the belly; cut on either side of this row and pull the strip out. Carefully drop the fish into the saucepan, then gently and briefly turn it through the vegetables. Add enough water to just cover the fish. When all the liquid comes up to a simmer, barely cook the fish (for no more than 4 minutes), as you really want it to be as tender as possible. Remember that in the time it takes to add the cream and then serve the soup it will still be cooking.
Pour in the cream and stir it through oh so delicately so as not to break up the fish. Taste the stock to check the seasoning. Scatter the dill over the soup. Need I say … serve promptly.