Put the salt cod in a saucepan with enough water to cover it and add a bay leaf. Bring to just under the boil, take the pan off the heat, put a lid on it and leave to sit for 10 mins. Lift the fish out onto a plate, reserving the cooking water. Flake the cod, removing the skin. Cook the potatoes in the salt cod cooking water until tender, about 12 mins depending on size. Drain, then put a clean tea towel over the pan, cover and leave for 5 mins or so (this helps the potatoes dry out a bit).
Bring 300ml water and the olive oil to the boil in a saucepan. Take the pan off the heat and immediately add the flour in a slow stream, whisking (use a balloon whisk) as you do so. You will end up with a batter, if it is a little lumpy, beat it hard. Leave to cool for about 5 mins. Beat in the eggs, a little at a time, until you have a smooth mixture – you need to beat hard.
Mash the potatoes with the salt cod, garlic, parsley, lemon juice and seasoning (even though you are using salt cod, this needs good seasoning). Beat the mixture into the batter, then cook over a low heat for about 8 mins, stirring all the time. The mixture should thicken considerably and come away from the sides of the pan. Put in a bowl, cover and leave to cool completely. Form the mixture into balls, bigger than walnuts but not as big as golf balls.
To make the allioli, gently heat the lemon juice and vinegar in a small pan. Add the saffron, stir to help it dissolve and leave it to sit for 15 mins. Put the garlic on a chopping board and, using salt as an abrasive, crush them to a paste. Put the egg yolks and garlic in a bowl. Using an electric whisk, slowly add the olive oil a drop at a time. As the mixture starts to thicken, you can increase the quantity. Gradually add the saffron mixture, then taste and season (the seasoning and how much lemon juice you use is really important).
Heat the oil in a deep saucepan (fill it no more than a third full) until it reaches 190C on a thermometer or a cube of bread browns in 30 seconds. Deep-fry the balls, in batches, for 4 mins, or until deep golden. Drain on a double layer of kitchen paper and serve hot with the allioli and lemon wedges.