Bring a large pot of salted water to the boil. Add potatoes; cook until tender but still firm, about 15 minutes. Drain and transfer to a large bowl.
Place eggs in a saucepan and cover completely with cold water. Bring water to the boil. Cover, remove from heat and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water and cool. Peel, chop and add to potatoes.
In a small bowl, combine lemon juice, oil, sugar, salt, Worcestershire sauce, mustard and black pepper; mix well. Blend in mayonnaise. Pour lemon dressing over potatoes and stir to coat.
Mix in spring onions, celery and parsley. Refrigerate for at least 2 hours before serving to allow flavours to meld.