Cut the pastry into 6 pieces, then roll each piece out thinly on a lightly floured surface until a little larger than a buttered 10 cm (4 inch) fluted loose-bottomed tart tin. Lift into the tins, press over the base and sides, then trim the excess pastry with scissors so it stands a little above the top of the tin. Put on a baking sheet, prick the bases with a fork, then chill for 15 minutes.
Line the tarts with nonstick baking paper and baking beans and bake blind in a preheated oven, 190°C (375°F), Gas Mark 5 for 8 minutes, then remove the paper and beans and cook for a further 4 minutes until golden. Leave to cool.
Whisk the cream in a bowl until it foms soft swirls. Add the condensed milk and lime rind and whisk to mix. Gradually whisk in the lime juice until thick. Spoon into the tart cases and chill until ready to serve.
Mix the cornflour and the measurement water to a smooth paste in the base of a small saucepan, add the blueberries and sugar and cook for 2–3 minutes until the blueberries just begin to soften and the juices run. Leave to cool.
When ready to serve, remove the tarts from the tins and spoon the blueberry compote on top.