Preheat oven to 220 C / Gas 7; position rack in the bottom third of oven.
Whisk 300g plain flour, 2 tablespoons sugar, 1 teaspoon cinnamon, 1 1/2 teaspoons salt and cream of tartar in a large bowl. Drizzle in butter. Stir mixture until just combined and crumbly.
Transfer 1/2 of the mixture into a separate bowl; add the remaining 3 tablespoons sugar and 1 teaspoon cinnamon. Knead with your fingertips until well combined but still crumbly. Cover with clingfilm; freeze crumble topping until ready to use.
Pour vinegar and water into the remaining base mixture. Mix to form a dough; transfer to a lightly floured work surface and knead until smooth. Press dough onto the bottom and sides of a pie dish. Crimp edges with a lightly floured fork. Freeze until ready to use.
Toss apples, 100g caster sugar, 3 tablespoons flour, 1 teaspoon cinnamon and sea salt together in a large bowl. Pile over the base and cover with the crumble topping.
Bake on the bottom rack of the preheated oven until lightly browned, about 20 minutes.
Reduce oven temperature to 170 C / Gas 3. Turn tart and continue baking, covering edges with foil halfway through, until edges are golden brown, about 50 minutes. Cool on a wire rack before slicing, about 1 hour.
The pastry and crumble topping can be made in advance and frozen for up to 3 months; thaw in fridge before using.