Put the apples in a saucepan with the blackberries, water and sugar. Cover and cook gently for 5-10 minutes, stirring occasionally, until the fruit is soft.
Process in a food processor and then pass it through a fine sieve to remove the pips. Allow to cool then chill thoroughly.
Divide between six shallow bowls then carefully pour in the custard in swirls. Drag randomly with a knife to give a muddling effect.