Bring a large pan of salted water to the boil. Wash your potatoes and halve any larger ones. Place them in the boiling water, bring back to the boil then cook for 12 to 15 minutes, or until cooked through.
Trim and finely slice the spring onions, then pick and finely chop the parsley.
Chop the chorizo into small chunks and place in a cold pan on a medium heat and fry till the fat renders out and the pieces are lovely and crispy.
Spoon the chorizo into a large bowl and give the pan a wipe. Add the spring onions and parsley to the bowl with the chorizo.
When the potatoes are done, drain in a colander, leave to steam dry, then add to the bowl with the chorizo. Squeeze in the juice of 1 lemon and pour in a good lug of extra virgin olive oil. Season well with salt and pepper, and toss to combine.
Put your chorizo pan back on a high medium high heat. Season the mackerel with sea salt and black pepper, then place skin-side down in the hot pan. Fry for about 8 minutes then turn over and cook for a further 2 minutes.
Serve the mackerel and chorizo with the remaining lemon, cut into wedges for squeezing over, and the potato salad.