Place the shallot, garlic and white wine in a large saucepan and bring to the boil. Add the mussels, cover and cook for 4 to 5 minutes, shaking the pan a few times until the mussels have opened. Remove the mussels from the saucepan and discard any that have not opened. Reserve the cooking liquid in the saucepan and add in the hake. Cover and cook gently for 3-4 minutes until the hake is just cooked through - don't allow it to boil. Put a large colander over a bowl and tip the fish into the colander, allowing the liquid to strain into the bowl. Break the hake into chunks.
Meanwhile cook the linguine as per packet instructions. When the pasta is cooked, drain, saving a couple of tablespoons of the cooking liquid. Return the pasta to the saucepan along with the reserved cooking liquid.
Rinse the saucepan the mussels and hake were cooked in, then pour the reserved cooking liquid from the bowl back into the saucepan, leaving any fine grit in the bottom of the bowl. Simmer for a minute or two, then pour in the cream and simmer to reduce a little. Add the cheese, stir and allow it to melt. Add the capers and stir through. Pour the sauce into the sauce pan with the pasta along with the mussels and chunks of hake and mix gently. Return the saucepan to a low heat for a couple of minutes to heat through. Taste and season with a little salt and black pepper.