Wash the rice under cold running water and drain well.
Place the milk in a heavy-based saucepan. Bring to boiling point then pour in the rice in a stream. Cover and cook gently for around 25 minutes.
Add the grated coconut, caster sugar and vanilla sugar. Blend in well, cover and cook gently for around 5 minutes. Divide the coconut rice among small serving bowls and leave to cool, then refrigerate.
Peel and quarter the peaches. Process them to a fine purée and sprinkle with lemon juice.
Serve the chilled rice with the peach purée.