Cook the potatoes in a large saucepan of lightly salted water for about 20 minutes until just tender. Take care not to overcook or the skins will split. Drain well, allow to cool slightly, then cut the potatoes into quarters.
Meanwhile, half-fill a large frying pan with water. Add the chicken fillets and poach for 10–15 minutes over a moderate heat until cooked through.
Remove the chicken from the pan with tongs or a slotted spoon. Cover and allow to cool slightly. Once it is cool enough to handle, slice it into pieces on the diagonal.
Cook the bacon in a dry frying pan over a moderate heat until crisp and brown. Drain on paper towels.
Put the potato pieces, chicken, half the bacon and the semi-dried tomatoes and salad greens into a bowl. Gently toss to combine.
Drizzle with the dressing and toss with the eggs and the remaining bacon, then serve warm or cold.