Sift the flour into a bowl and rub in the butter until the mixture resembles fine breadcrumbs. Make a well in the centre and stir in enough of the milk to give a fairly soft dough. Turn it out on to a lightly floured surface and knead gently. Cut into 4 pieces, then knead again to shape each into a rough round. Roll out 4 rough circles each to about 15 cm (6 inch) and place on a baking sheet.
Mix together the passata, tomato purée and basil. Divide between the scone bases and spread to within 1 cm (½ inch) of the edges. Pile each with the ham and olives, then sprinkle with the mozzarella.
Drizzle with a little oil and bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 15–20 minutes until the bases are risen and the cheese is golden. Wrap in foil and serve warm or cold.