Cook the potatoes in boiling salted water and until tender - about 10 to 15 minutes.
While the potato is cooking, make the mayonnaise. Place the egg yolk in a mixing bowl with the lemon juice. Gradually whisk in the vegetable oil in a slow stream until the mixture reaches the correct consistency. Set aside.
Drain the potatoes, and when cool enough to handle, slice thinly. Place in a large bowl and add the spring onions, gherkins and radishes.
Mix all the dressing ingredients together in a small bowl and pour over the potato salad. Sprinkle with the dill and add the mayonaise, and mix gently. Season to taste with salt and freshly ground black pepper. Refrigerate and serve chilled.