Preheat the oven to 130C/250F/Gas½. Line a 24cm/9.5in spring-form cake tin with parchment paper.
For the cheesecake base, place the digestive biscuits in a large ziplock bag. Using a roller pin, break the digestive biscuit until breadcrumb-like. In a large bowl, mix the digestive biscuits and melted butter. Then take a parchment paper and press the mixture using your fingers into the bottom of the lined cake tin. Make sure to even out the biscuit mixture. Place in the fridge for 15-20 minutes to set whilst you make the rest of the cake.
For the blackberry purée, place the berries and sugar into a saucepan along with a splash of water and simmer over medium-low heat until the berries break down and become tender. Set aside to cool.
For the cheesecake filling, gently beat into the cream cheese and vanilla extract until well combined. In a jug, whisk together the eggs, lemon juice and double cream.
Add half of the egg mixture to the cream cheese and mix together until smooth and well combined. Add the flour and sugar to the cream cheese mixture, then mix in the remaining egg mixture until smooth.
Pour the cheesecake mixture into the prepared tin, then drizzle over the blackberry purée. Bake the cheesecake for 60 - 75 minutes, or until the cheesecake is set and lightly golden on top. Set aside to cool. Garnish with blackberries.