Preheat oven to 230ºC. Grease a large baking tray.
Sift the flours and baking powder into a bowl; tip in any bran left in the sieve. Rub in butter with fingertips until mixture resembles fine breadcrumbs.
Add the rolled oats, watercress and about three-quarters of the cheese; season with salt and black pepper. Stir in the milk with a fork. Scrape the dough together with a spatula and turn out onto a well-floured work surface. Shape into a smooth, soft ball; it will be a little softer than a standard scone dough.
Pat or roll out the dough to 2 cm thick. Use a 7.5 cm round cutter to stamp out scones. Press the trimmings together lightly, re-roll and stamp out more scones.
Place the scones on the baking tray, arranging them so they are not touching. Brush the tops lightly with milk and sprinkle with the remaining grated cheese. Bake for 10–15 minutes or until risen and golden brown. Cool on a wire rack. These scones are best eaten on the day they are made.