Place potatoes in a large saucepan, cover with cold, salted water, bring to the boil, then reduce heat to medium and simmer until tender (about 10-15 minutes). Drain, cool slightly, then peel and thickly slice widthways.
Meanwhile, bring another saucepan of water to the boil, add eggs and cook for 4 minutes. Remove and cool under cold running water, then peel and set aside.
For salad cream, combine ingredients in a small bowl and season to taste with sea salt and freshly ground black pepper.
Add smoked fish to potato and season to taste. Top rye bread with smoked fish mixture, then drizzle with salad cream. Halve soft-boiled eggs, arrange on fish mixture, spoon over salmon roe and serve.