Bring a medium saucepan (16-18cm or 7") pan of water to a boil and season with three-quarters of a teaspoon of salt. Add the potatoes and boil for 18-20 minutes.
Remove the skin from the chorizo and break it up into 1-2cm (½"-¾") chunks.
Pat the hake dry with some kitchen paper, paying particular attention to the skin.
When the potatoes are cooked drain them and lightly crush them with the bottom of a glass.
Heat two frying pans on the hob, the pan for the fish needs to be on a high-medium heat and the pan for the chorizo on a medium-high heat.
Add the pieces of chorizo to the pan and cook for 3-5 minutes (stirring occasionally) or until it begins to colour and begins to leach oil.
Throw in the potatoes and cook for another 5 minutes, tossing occasionally.
Whilst the potatoes are cooking season the fish with the remaining salt and place it skin side down and let it sit for 3 minutes.
Flip the fish and add the butter, when the butter melts use it to baste the fish for another 2-3 minutes before removing and resting for 1 minute.
Add the sherry vinegar and samphire to the potato and chorizo mix, toss to combine, then cook for a final minute then serve.
