Cook the potatoes in a large pan of boiling, salted water for 10-12 minutes , until tender. Drain, leave to steam dry and cool completely.
Meanwhile, cook the eggs in a pan of boiling water for eight minutes. Drain and run under cold water until completely cool. Drain, peel and roughly chop the eggs.
Mix the mayonnaise, yogurt and horseradish in a large bowl, season with salt and pepper and most of the spring onions.
Tip the cooked potatoes into the mixture along with the chopped beetroot and gently toss to coat in the dressing. Sprinkle over the hard-boiled egg and remaining spring onions and serve.