Preheat the oven to 180 C / Gas 4. Line a 20x30cm baking tin with tin foil leaving a good amount over overhang over the sides.
Place 300g of the blueberries in a food processor and blend until smooth. Press through a sieve into a clean saucepan. Dissolve the cornflour in a little cold water then add to the blueberry purée. Cook and stir for 8 to 10 minutes over a low heat until thickened. Remove from the heat and allow to cool.
Combine the biscuit crumbs and butter in small bowl and mix well. Press evenly into the bottom of the prepared baking tin.
In large bowl, beat the cream cheese until fluffy. Gradually beat in condensed milk until smooth. Add eggs, lemon juice and vanilla. Beat until thick and creamy. Pour over prepared base.
Drop the blueberry purée mixture by spoonfuls onto the cheesecake. Gently swirl with a knife to create a marbled effect.
Bake 25 to 30 minutes until centre is set. Cool completely to room temperature and then in the fridge for 3 hours. Cut into slices or squares and serve with the remainder of fresh blueberries.