First make the compote. Place the apricots and sugar in a pan over a low heat for about 45 minutes. Stir now and then very gently, so that the apricots remain relatively whole. Transfer to a bowl, cool and chill in the refrigerator.
While the compote is simmering, place the blueberries (reserving a few for garnish), water and sugar in a saucepan. Simmer over medium heat for 10 minutes, stirring occasionally.
Mix the flour, sour cream and salt in a bowl and whisk until smooth. Pour in one cup of the hot blueberry mix and whisk vigorously.
Now add the mixture to the simmering blueberries, stir well and continue to simmer for 10 minutes until the soup thickens.
Blend in a food processor until smooth. Transfer to a bowl and leave to cool with cling film resting on the surface to prevent a skin forming. Chill until serving.
Serve the blueberry soup chilled, garnished with whole blueberries and a blob of compote in the middle of each bowl. Enjoy the remaining compote with yogurt.