Wash the Jersey Royal potatoes and slice any large ones in half. Gently boil the potatoes in salted water until tender. Drain, run under cold water and leave to cool.
To make the dressing, add all ingredients to a blender or food processor and blitz until smooth.
Pour the dressing over the cooled potatoes and toss to coat. Keep refrigerated until ready to serve.
Just before serving, cut the avocado flesh into chunks and pile onto the dressed salad then sprinkle with the sliced radishes, parsley and basil.