Add about a teaspoon (large pinch) of saffron threads to the left-over liquid from boiling the mussels and over medium-high heat and bring to a gentle simmer for about a minute.
Once simmering, add the double cream and stir all the ingredients together over medium heat. You don't want this to reach a hard boil, as the cream will separate.
Now, add the remaining 50ml of dry white wine, freshly chopped parsley, salt and freshly ground black pepper. Mix together and cook over medium heat for another minute or two.
By this point the spaghetti should be finished cooking. Drain it in a colander. Shake the excess water out, as you don't want your cream sauce to be too watery.
Add the spaghetti to your saffron cream sauce and mix together. Then cover the spaghetti and sauce with the cooked mussels.
Finally, gently combine the mussels with the saffron spaghetti cream sauce and season with more salt, pepper and freshly chopped parsley.