Preheat the oven to 190°C/fan 170°C/gas mark 5. Mix together the plain flour, wholemeal flour, bicarbonate of soda, cream of tartar and sugar in a large bowl with 1 tsp salt. Add the butter and rub in, using your fingertips, until the mixture resembles breadcrumbs.
Stir in the buttermilk and milk to mix to a stiff consistency, taking care not to over-mix. Add more milk if necessary. Knead very lightly on a floured surface and shape into a ball.
Place the dough on a lightly floured baking sheet. Cut a 2½cm-deep cross in the centre and bake in the oven for 25-30 minutes until risen and golden and the centre of the cross feels firm. Remove from the oven and wrap in a clean tea towel to cool.