Place in a lightly oiled bowl, cover with clingfilm and set aside until doubled in size, about 1-2 hours. You can also place the dough in the fridge to rise overnight, in which case, allow it to come up to room temperature for half an hour before rolling it out.
While the dough is rising make the candied oranges. Slice the ends off the oranges then cut them into thin slices, about 3-6mm/1/8-1/4 inch thick.
Place the sugar and water in a pan and heat gently while stirring until the sugar has dissolved. Add the orange slices and bring up to a simmer, leave to simmer gently for 40-60 minutes, until the liquid has reduced to a thick syrup and the oranges are soft and the peel has become slightly translucent. Turn the slices occasionally to unsure that they are evenly covered.
Tip the risen dough out onto a lightly floured surface and roll it out to about 1cm/3/8 inch thick. Use an approx 7cm/2.75 inch round pastry cutter to cut out circles of dough, then use a 2.5cm/1 inch one to cut a hole out of the centre of each (I used the wide end of a piping nozzle as I didn't have a cutter small enough). Knead together the scraps until smooth then re-roll the dough and cut out more rounds; you should be able to get about 10 doughnuts. I like to fry up the doughnut holes too so save them if you like.
Heat a deep fat fryer or large pan of oil to 165-170C/335-340F. Cut the paper around each doughnut so that each one is sitting on it's own square of paper. Lift the doughnut on it's parchment into the oil; the paper will come away from the doughnut and you can fish it out with tongs. I find this the easiest way to transfer the doughnuts into the fryer as they are quite soft and sticky.
Fry the doughnuts two at a time for a couple of minutes per side until golden, they should reach 100C/212F inside, I use a probe thermometer to check each one is done. Use a slotted spoon to lift the doughnuts out onto a plate lined with kitchen paper to drain.