Thickly slice the potatoes and place in a pan. Cover with boiling water from the kettle, return to the boil and simmer for 15 minutes or until the potatoes are just tender.
While the potatoes cook, remove the skin from the mackerel and discard. Break the flesh into bite sized pieces and place in a large bowl.
Halve the cucumber and use a teaspoon to scoop out the seeds. Finely chop the cucumber flesh and add to the bowl. Add the lemon zest and juice and chives to the bowl and mix well.
Drain the potatoes in a colander, then add to the bowl and mix everything together. Season to taste. Serve with a crisp watercress salad.