Mix the flours with the salt, yeast (even if using fresh, just crumble it in) and sugar in a large bowl or the bowl of a standing mixer. Add the oil and water and mix to a soft sticky dough. Leave for 10 minutes, then knead briefly by hand or mix with a dough hook attachment. Leave for another 10 minutes, then repeat the kneading twice again. The final dough should be smooth, elastic and stop sticking to your hands and bounce off the sides of the bowl in a standing mixer. Leave covered for 30 minutes.
Preheat the oven to your highest setting (250C/485F/gas 9, or whatever you can get). Place a baking sheet in the oven to get it very hot.
Turn the rested dough onto a floured surface and divide into 9-10 pieces, about 90g each. Shape them into balls, cover with a clean tea towel and leave to rest for 15 minutes. Roll out each ball, one or two at a time, reasonably thin, into oval shapes – about 5mm thick.
Place one or two pitas on the preheated baking sheet and bake for 3 to 5 minutes until they puff up and only just start to colour. Cool on a wire rack covered with a cloth, to keep them moist.
