Sift the flour into a large mixing bowl and add the sugar, baking powder, baking soda, and ¾ teaspoon salt in a large bowl. Cut in the butter with a pastry blender or rub in with your fingers. (The largest pieces should be the size of small peas.) With your fingertips, flatten the butter pieces into small disks. Cover with plastic wrap, and refrigerate for about 20 minutes until the butter is very firm.
Combine the cream and vanilla in a small bowl, and stir into the flour mixture with a wooden spoon until almost absorbed and the dough just comes together. Turn out the dough onto a lightly floured work surface and roll it out into a 20cm x 25cm (8" x 10") rectangle. With a short side facing you, fold the rectangle into thirds, as you would a letter.
Rotate the dough a quarter turn clockwise. Repeat rolling out, folding, and rotating dough 2 more times. With floured hands, pat out dough to a 3cm (1¼") thickness, and cut out as many rounds as possible with a floured 5.5cm (2¼") round biscuit cutter. Gather the scraps, reroll once, and cut out more rounds (you should have a total of about 12).
Place the scone doughs 5cm (2") apart on parchment-lined baking sheet(s). Brush the tops with cream, and sprinkle with sugar. Bake in a preheated moderately hot oven (Mk 5 - 375ºF - 190ºC) for 18 to 20 minutes, rotating the sheets halfway through. Remove from the oven and allow them to cool on the sheets. Serve warm or at room temperature.