Place all the ingredients for the sauce in a small saucepan and simmer over a low heat, stirring occasionally, for 5 minutes. Leave to cool.
Meanwhile, make the base. Place the flour and salt in a large bowl, then rub in the butter with your fingertips. Slowly pour in the milk and mix to form a soft dough.
Roll out the dough thinly on a large, lightly oiled baking sheet into a 30 cm (12 inch) round. Spread the tomato sauce over the pizza base and sprinkle with the Cheddar. Arrange the mozzarella and tomatoes over the top and drizzle over the pesto.
Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 15 minutes until the base is crisp and the cheese has melted. Serve hot with basil leaves scattered over.